Lion 's mane jellyfish - wikipedia Lion 's mane jellyfish Jump to : navigation , search Lion 's mane jellyfish Scientific classification Kingdom : Animalia Phylum : Cnidaria Class : Scyphozoa Order : Semaeostomeae Family : Cyaneidae Genus : Cyanea Species : C. capillata Binomial name Cyanea capillata ( Linnaeus , 1758 ) The lion 's mane jellyfish ( Cyanea capillata ) , also known as the giant jellyfish or the hair jelly , is the largest known species of jellyfish . Its range is confined to cold , boreal waters of the Arctic , northern Atlantic , and northern Pacific Oceans . It is common in the English Channel , Irish Sea , North Sea and in western Scandinavian waters south to Kattegat and Øresund . It may also drift in to the south - western part of the Baltic Sea ( where it can not breed due to the low salinity ) . Similar jellyfish -- which may be the same species -- are known to inhabit seas near Australia and New Zealand . The largest recorded specimen found washed up on the shore of Massachusetts Bay in 1870 , had a bell with a diameter of 2.3 metres ( 7 ft 6 in ) and tentacles 37.0 m ( 121.4 ft ) long . Lion 's mane jellyfish have been observed below 42 ° N latitude for some time in the larger bays of the east coast of the United States . The lion 's mane jellyfish uses its stinging tentacles to capture , pull in and eat prey such as fish , sea creatures and smaller jellyfish . Contents ( hide ) 1 Taxonomy 2 Description 3 Ecology 4 Behavior and reproduction 5 Sting and human contact 6 In popular culture 7 Gallery 8 References 8.1 Other sources 9 External links Taxonomy ( edit ) Cyanea sp . The taxonomy of the Cyanea species is not fully agreed upon ; some zoologists have suggested that all species within the genus should be treated as one . Two distinct taxa , however , occur together in at least the eastern North Atlantic , with the blue jellyfish ( Cyanea lamarckii Péron & Lesueur , 1810 ) differing in color ( blue , not red ) and smaller size ( 10 -- 20 cm diameter , rarely 35 cm ) . Populations in the western Pacific around Japan are sometimes distinguished as Cyanea nozakii , or as a subspecies , C. c. nozakii . In 2015 , Russian researchers announced a possible sister species , Cyanea tzetlinii found in the White Sea , but this has not yet been recognized by other authoritative databases such as WoRMS or ITIS . Description ( edit ) Lion 's mane jellyfish ( Cyanea capillata ) are named for their showy , trailing tentacles reminiscent of a lion 's mane . They can vary greatly in size : although capable of attaining a bell diameter of over 2 metres ( 6 ft 7 in ) , those found in lower latitudes are much smaller than their far northern counterparts , with a bell about 50 centimetres ( 20 in ) in diameter . Size seems to dictate coloration : larger specimens are a vivid crimson to dark purple while smaller specimens grade to a lighter orange or tan , occasionally colorless . The bell of the lion 's mane jellyfish is scalloped into eight lobes ( lappets ) , each lobe containing from 70 to 150 tentacles , arranged in four fairly distinct rows . Along the bell margin is a balance organ at each of the eight indentations between the lobes -- the rhopalium -- which helps the jellyfish orient itself . From the central mouth extend broad frilly oral arms with many stinging cells . Closer to its mouth , its total number of tentacles are around 1200 . The long , thin tentacles which emanate from the bell 's subumbrella have been characterised as `` extremely sticky '' ; they also have stinging cells . The tentacles of larger specimens may trail as long as 30 m ( 100 ft ) or more , with the tentacles of the longest known specimen measured at 37 m ( 120 ft ) in length . This unusual length -- longer than a blue whale -- has earned it the status of one of the longest known animals in the world . Ecology ( edit ) As coldwater species , these jellyfish can not cope with warmer waters . The jellyfish are pelagic for most of their lives but tend to settle in shallow , sheltered bays towards the end of their one - year lifespan . In the open ocean , lion 's mane jellyfish act as floating oases for certain species , such as shrimp , medusafish , butterfish , harvestfish , and juvenile prowfish , providing both a reliable source of food and protection from predators . Predators of the lion 's mane jellyfish include seabirds , larger fish such as ocean sunfish , other jellyfish species , and sea turtles . The leatherback sea turtle feeds almost exclusively on them in large quantities during the summer season around Eastern Canada . The jellyfish themselves feed mostly on zooplankton , small fish , ctenophores , and moon jellies . Behavior and reproduction ( edit ) Main article : Jellyfish § Life cycle Lion 's mane jellyfish swimming , side view Lion 's mane jellyfish remain mostly very near the surface , at no more than 20 m depth . Their slow pulsations drive them forwards weakly , so they depend on ocean currents to travel great distances . The jellyfish are most often spotted during the late summer and autumn , when they have grown to a large size and the currents begin to sweep them to shore . Like other jellyfish , lion 's manes are capable of both sexual reproduction in the medusa stage and asexual reproduction in the polyp stage . Lion 's mane jellyfish have four different stages in their year - long lifespan : a larval stage , a polyp stage , an ephyrae stage , and the medusa stage . The female jellyfish carries its fertilized eggs in its tentacle , where the eggs grow into larva . When the larva are old enough , the female deposits them on a hard surface , where the larva soon grow into polyps . The polyps begin to reproduce asexually , creating stacks of small creatures called ephyrae . The individual ephyrae break off the stacks , where they eventually grow into the medusa stage and become full grown jellyfish . Sting and human contact ( edit ) Most encounters cause temporary pain and localized redness . In normal circumstances , and in healthy individuals , their stings are not known to be fatal . Vinegar can be used to deactivate the nematocysts , but due to the large number of tentacles medical attention is recommended after exposure . There may be a significant difference between touching a few tentacles with finger tips at a beach , compared to an accidental swimming into one . The initial sensation is more strange than painful , it feels like swimming in to a bit warmer and somewhat effervescent water . Some minor pains will though soon follow . It 's not a pleasant feeling , and especially not for children . Normally there is no real danger to humans ( with exception of people suffering from special allergy ) . But in cases when someone has been stung over large parts of his / her body , and not just by the longest tentacles , but by the whole jellyfish ( including the inner tentacles , of which there are around 1200 ) , a visit to a health care centre or similar is recommendable . Although rare , at deep water severe stings can also cause panic followed by drowning . To confuse a Lion 's Mane sting with other Bell jellyfish is perhaps not of larger importance ( although this field is poorly investigated ) , but to assume a sting from a Portuguese man o ' war and usually even worse , from any Box jellyfish especially like the Sea Wasp , to be a Lion 's Mane , can be lethal . Though any contact with the latter one is so extremely painful and very deadly that it immediately becomes obvious . On a July day in 2010 , around 150 beachgoers were stung by the remains of a lion 's mane jellyfish that had broken up into countless pieces in Wallis Sands State Beach , Rye , New Hampshire , in the United States . Considering the size of the species , it is possible that this mass incident was caused by a single specimen . In popular culture ( edit ) The lion 's mane jellyfish appears in the Sherlock Holmes short story `` The Adventure of the Lion 's Mane '' published in The Case - Book of Sherlock Holmes . Holmes discovers at the end of the story that the true killer of a professor who died shortly after going swimming ( shouting `` the lion 's mane '' before he succumbed ) was actually this jellyfish . Suspicion was originally laid upon the professor 's rival in love , until the latter was similarly attacked ( he survived , although badly stung ) . In the context of the story , it is only because the school professor has a weak heart that he succumbs , as is confirmed by the survival of the second victim . A photograph widely distributed on the internet appears to show an anomalously large lion 's mane dwarfing a nearby diver by several times . The photo was subsequently shown to be a hoax . On the popular television program QI the show claimed that the longest animal in the world was the lion 's mane jellyfish . This was later corrected -- in 1864 , a bootlace worm ( Lineus longissimus ) was found washed up on a Scottish shore that was 55 m ( 180 ft ) long . ( That claim has its critics : because bootlace worms can easily stretch to several times their natural length , it is possible the worm did not actually grow to be that length . ) Gallery ( edit ) A lion 's mane jelly capturing a sea gooseberry Lion 's mane jellyfish with full threads visible Lion 's mane jellyfish contracted Lion 's mane jellyfish in star formation Lion 's mane jellyfish open , showing underside Life - sized model in the Smithsonian Museum of Natural History , Washington DC , US Small , dead lion 's mane jelly washing up on the beach Blue lion 's mane jellyfish in Askeröfjorden outside Stenungsund , Sweden . References ( edit ) Jump up ^ Hair Jelly ( Cyanea capillata ) . Australian Venom Research Unit . ^ Jump up to : `` Lion 's Mane Jellyfish -- Reference Library '' . redOrbit . Retrieved 2010 - 09 - 03 . Jump up ^ `` Lion 's Mane Jellyfish : Discovery Channel '' . Dsc.discovery.com. 2013 - 05 - 23 . Retrieved 2013 - 09 - 08 . Jump up ^ Glafira D. Kolbasova ; Arthur O. Zalevsky ; Azamat R. Gafurov ; Philipp O. Gusev ; Margarita A. Ezhova ; Anna A. Zheludkevich ; Olga P. Konovalova ; Ksenia N. Kosobokova ; Nikita U. Kotlov ; Natalia O. Lanina ; Anna S. Lapashina ; Dmitry O. Medvedev ; Katerina S. Nosikova ; Ekaterina O. Nuzhdina ; Georgii A. Bazykin ; Tatyana V. Neretina ( 2015 ) . `` A new species of Cyanea jellyfish sympatric to C. capillata in the White Sea '' . Polar Biol . doi : 10.1007 / s00300 - 015 - 1707 - y . Jump up ^ `` Lion 's Mane Jellyfish '' . Scubatravel.co.uk . Retrieved 2010 - 09 - 03 . Jump up ^ https://web.archive.org/web/20110108024017/http://www.typesofjellyfish.net/lions_mane_jellyfish/lions_mane_jellyfish.html Jump up ^ Kozloff , Eugene ( 2003 ) . Seashore Life of the Northern Pacific Coast . University of Washington Press . pp. 54 , 56 ( 1983 edition ) . ISBN 0295960841 . Jump up ^ Point 6 at ^ Jump up to : `` Lions Mane Jellyfish '' . Types Of Jellyfish . Archived from the original on 2011 - 01 - 08 . Retrieved 2010 - 09 - 03 . Jump up ^ Heaslip SG , Iverson SJ , Bowen WD , James MC ( 2012 ) Jellyfish Support High Energy Intake of Leatherback Sea Turtles ( Dermochelys coriacea ) : Video Evidence from Animal - Borne Cameras . PLoS ONE 7 ( 3 ) : e33259 . doi : 10.1371 / journal. pone. 0033259 Jump up ^ `` Giant Jellyfish '' . Extremescience.com . Retrieved 2010 - 09 - 03 . Jump up ^ `` SCDNR -- Jelly fish '' . Dnr.sc.gov . Retrieved 2010 - 09 - 03 . Jump up ^ `` Open ocean -- Jellyfish life cycle -- Te Ara Encyclopedia of New Zealand '' . Teara.govt.nz. 2009 - 03 - 02 . Retrieved 2010 - 09 - 03 . Jump up ^ `` Lion 's Mane Jellyfish '' . Jellyfishfacts.net . Retrieved 2010 - 09 - 03 . ^ Jump up to : http://mentalfloss.com/article/61609/15-facts-about-lions-mane-jellyfish Jump up ^ https://www.mayoclinic.org/diseases-conditions/jellyfish-stings/symptoms-causes/syc-20353284 Jump up ^ https://www.siliconrepublic.com/innovation/jellyfish-sting-vinegar-lions-mane Jump up ^ `` 150 Stung By Jellyfish At Rye Beach -- New Hampshire News Story -- WMUR Manchester '' . Wmur.com. 2010 - 07 - 21 . Archived from the original on 2011 - 10 - 14 . Retrieved 2010 - 09 - 03 . Jump up ^ http://www.hoaxorfact.com/pranks/picture-of-giant-lion-s-mane-jellyfish-facts.html Jump up ^ Carwardine , M. 1995 . The Guinness Book of Animal Records . Guinness Publishing . p. 232 . Other sources ( edit ) British Marine Life Study Society -- C. capillata and C. lamarcki Marine Life Information ( UK ) Marine Biological Laboratory ( Massachusetts ) Pacific Coast jellies External links ( edit ) Wikimedia Commons has media related to Cyanea capillata . Taxon identifiers Wd : Q522939 ADW : Cyanea_capillata ARKive : cyanea - capillata BioLib : 126478 EoL : 1005690 EPPO : CYNECA Fauna Europaea : 240643 GBIF : 2264478 iNaturalist : 69838 ITIS : 51671 NCBI : 27804 WoRMS : 135301 Retrieved from `` https://en.wikipedia.org/w/index.php?title=Lion%27s_mane_jellyfish&oldid=834313563 '' Categories : Semaeostomeae Animals described in 1758 Hidden categories : Articles with ' species ' microformats All articles with unsourced statements Articles with unsourced statements from February 2012 Talk Contents About Wikipedia Wikispecies Azərbaycanca Català Cebuano Čeština Dansk Deutsch Español Esperanto فارسی Français Frysk Gaeilge 한국어 Bahasa Indonesia Íslenska Italiano עברית Lietuvių Magyar Nederlands Norsk Norsk nynorsk پنجابی Polski Português Română Русский Simple English Suomi Svenska Türkçe Tiếng Việt Winaray 中文 26 more Edit links This page was last edited on 5 April 2018 , at 01 : 30 . 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Question: which is the lion's mane jellyfish's species within its genus


Super Bowl XXXVII - wikipedia Super Bowl XXXVII Jump to : navigation , search Super Bowl XXXVII Oakland Raiders ( AFC ) Tampa Bay Buccaneers ( NFC ) 21 48 Total OAK 0 6 12 21 TB 17 14 14 48 Date January 26 , 2003 ( 2003 - 01 - 26 ) Stadium Qualcomm Stadium , San Diego , California MVP Dexter Jackson , Safety Favorite Raiders by 4 Referee Bill Carollo Attendance 67,603 Future Hall of Famers Buccaneers : Derrick Brooks , Warren Sapp Raiders : Al Davis ( owner / general manager ) , Tim Brown , Jerry Rice , Rod Woodson Ceremonies National anthem Dixie Chicks Coin toss 1972 Miami Dolphins : Don Shula , Bob Griese , Larry Csonka , Larry Little , Jim Langer , Nick Buoniconti , Paul Warfield Halftime show Shania Twain , No Doubt , and Sting TV in the United States Network ABC Announcers Al Michaels , John Madden , Melissa Stark and Lynn Swann Nielsen ratings 40.7 ( est . 88.6 million viewers ) Market share 61 Cost of 30 - second commercial $2.1 million ← XXXVI Super Bowl XXXVIII → Super Bowl XXXVII was an American football game between the American Football Conference ( AFC ) champion Oakland Raiders and the National Football Conference ( NFC ) champion Tampa Bay Buccaneers to decide the National Football League ( NFL ) champion for the 2002 season . The Buccaneers defeated the Raiders by the score of 48 -- 21 , tied with Super Bowl XXXV for the seventh largest Super Bowl margin of victory , and winning their first ever Super Bowl . The game , played on January 26 , 2003 at Qualcomm Stadium in San Diego , California , was the sixth Super Bowl to be held a week after the conference championship games ( XVII , XXV , XXVIII , XXXIV , and XXXVI ) . It was also the last Super Bowl played in the month of January . Super Bowl XXXVI was the first to be played in February , due to the NFL postponing games for a week after the September 11 attacks . Starting with Super Bowl XXXVIII in 2004 , the Super Bowl has been permanently played in February . This was the last Super Bowl until Super Bowl 50 to take place in California . It was the first and only time until Super Bowl XLVIII in Super Bowl history that the league 's number one - ranked offense ( Raiders ) was pitted against the league 's number one - ranked defense ( Buccaneers ) . Super Bowl XXXVII is also referred to as the `` Pirate Bowl '' , due to both teams ' pirate - themed names . The game is sometimes referred to as the `` Gruden Bowl '' , because the primary storyline surrounding the game revolved around Jon Gruden . Gruden was the Raiders ' head coach from 1998 to 2001 , and then became the Buccaneers coach in 2002 . Tampa Bay , `` Gruden 's new team '' , made their first Super Bowl appearance in team history after posting a 12 -- 4 regular season record . Oakland , `` Gruden 's old team '' , advanced to their fifth Super Bowl after an 11 -- 5 regular season . This was also the first Super Bowl to feature two former division rivals , as the Buccaneers and Raiders both played in the AFC West in 1976 . The Raiders came into the game as four - point favorites . However , the Tampa Bay defense dominated the contest . Oakland quarterback Rich Gannon threw a Super Bowl record five interceptions , three of which were returned for touchdowns . The Buccaneers also sacked Gannon five times , and scored 34 consecutive points to build a 34 -- 3 lead late in the third quarter . Tampa Bay safety Dexter Jackson , who had two of those interceptions and returned them for 34 yards , was named Super Bowl MVP. Jackson became only the second safety and third defensive back named Super Bowl MVP . Contents ( hide ) 1 Background 1.1 Jon Gruden helps rebuild the Raiders 1.2 Gruden is `` traded '' to the Buccaneers 1.3 The Raiders win without Gruden 1.4 Playoffs 1.5 Super Bowl pregame news 2 Television and entertainment 2.1 Pregame ceremonies 2.2 Halftime show 2.3 Post-game ceremonies 3 Game summary 3.1 First Quarter 3.2 Second Quarter 3.3 Third Quarter 3.4 Fourth Quarter 3.5 Box score 3.6 Statistical overview 4 Final statistics 4.1 Statistical comparison 4.2 Individual leaders 5 Starting lineups 6 Post-game riots 7 Aftermath 8 Officials 9 Notes and references Background ( edit ) Super Bowl XXXVII was originally awarded to San Francisco on October 15 , 1997 by the NFL owners at a league meeting in Washington , D.C. The 49ers had recently announced plans for a new stadium , and were awarded the Super Bowl contingent on its completion . However , the stadium plans had stalled by the fall of 1998 and the NFL reopened the bidding for the game . San Diego , which had lost out on Super Bowl XXXVI , announced its interest . The city was awarded the game during the May 26 , 1999 meeting at Atlanta . Miami was the only other city in consideration . It was the last Super Bowl played in California until Super Bowl 50 at Levi 's Stadium in Santa Clara . It was the also the final Super Bowl at Qualcomm Stadium before the Chargers relocated to Los Angeles in 2017 . Later in 2003 , California would host the Stanley Cup Finals with the Mighty Ducks of Anaheim hosting games 3 , 4 , and 6 , making it only the second time that the same state hosted both the Super Bowl and the Stanley Cup Finals in the same year , following California itself ten years earlier , when the Los Angeles Kings went to the Finals four months after Pasadena hosted Super Bowl XXVII . It was then succeeded by itself again in 2016 when Super Bowl 50 took place in San Francisco and the San Jose Sharks made the Stanley Cup Finals . Jon Gruden helps rebuild the Raiders ( edit ) After moving back to Oakland , California in 1995 , the Raiders suffered sub-par seasons , including a 4 -- 12 record in 1997 . Under Gruden 's leadership , the Raiders improved to 8 -- 8 in both 1998 and 1999 . The team was further boosted in 1999 with the signing of veteran quarterback Rich Gannon . With Gannon as quarterback , the team jumped to the fifth - best offense in the league . The Raiders won the AFC West in 2000 with a 12 -- 4 record and the best rushing offense in the league . However , they lost the AFC Championship Game to the eventual Super Bowl XXXV champion Baltimore Ravens , 16 -- 3 . After signing veteran Pro Bowl wide receiver Jerry Rice and defensive tackle Trace Armstrong , the team repeated as AFC West champions in 2001 , but were eliminated in the AFC Divisional Game by the eventual Super Bowl XXXVI champion New England Patriots in what became known as the `` Tuck Rule Game '' , in which a potential game - ending fumble recovery by the Raiders was overturned by instant replay . Gruden is `` traded '' to the Buccaneers ( edit ) Further information : 2002 Tampa Bay Buccaneers season Raiders owner Al Davis was known to have the lowest salaries for coaches in the league , and Gruden was no exception . Instead of paying a high salary for Gruden , Davis opted to trade the rights for Gruden to the Buccaneers in exchange for four draft picks , in a deal similar to what Patriots owner Robert Kraft made with the New York Jets to get head coach Bill Belichick in 2000 . The Buccaneers ended up giving two first - round picks , two second - round picks and $8 million to the Raiders to get Gruden . Tampa Bay was desperate to have someone rebuild their offense so it would complement their powerful defense in an attempt to win the Super Bowl . For most of their history , the Buccaneers were regarded as losers , making the playoffs only three times in their first 20 seasons . But that changed when the team hired Tony Dungy as head coach in 1996 . Dungy , along with his defensive coordinator Monte Kiffin , rebuilt the defense around a core group of players , such as defensive lineman Warren Sapp , linebacker Derrick Brooks , and defensive backs Ronde Barber and John Lynch . By 1997 , Tampa Bay ranked 3rd in the league in total yards allowed , 2nd in 1998 , and 3rd in 2000 . With one of the best defenses in the league , Dungy helped guide the Buccaneers to four playoff appearances in his six years as the team 's head coach . But the team always had one of the worst offenses in the league , and this was a major factor in their playoff losses . Thus , Dungy was fired and replaced by Gruden . Still , even Gruden had trouble getting the offense in sync during his first year as Tampa Bay 's head coach . In 2002 , the Buccaneers ranked 25th in the league in total yards gained ( 5,222 ) . Quarterback Brad Johnson made the Pro Bowl , completing 281 out of 451 passes for 3,049 yards , 22 touchdowns , and only 6 interceptions . Running back Michael Pittman led the team in rushing with 718 yards and one touchdown , and caught 59 passes for 477 yards . Pro Bowl fullback Mike Alstott had 548 rushing yards and 5 touchdowns , and also had 35 receptions for 242 yards and 2 touchdowns . Wide receiver Keyshawn Johnson led the team with 76 receptions for 1,088 yards and 5 touchdowns , while wide receiver Keenan McCardell had 61 receptions for 670 yards and 6 touchdowns . However , the Buccaneers ' defense was still the strength of the team , leading the NFL in total defense ( 252.8 yards per game ) , pass defense ( 155.6 yards per game ) , points allowed ( 12.3 points per game ) , passing touchdowns allowed ( 10 ) , interceptions ( 31 ) , and opponent passer rating ( 48.4 ) . Brooks , Lynch , Sapp , and defensive end Simeon Rice all had Pro Bowl years . Brooks led the team with 87 tackles and excelled at pass coverage , recording 5 interceptions , 218 return yards , and 2 touchdowns , plus 1 fumble return and 1 on a lateral from Sapp after a Sapp interception for a total of 4 touchdowns ( an NFL record for a linebacker ) . The defense as a whole had nine total touchdowns during the regular season and playoffs . Rice led the team with 15.5 sacks . Sapp recorded 7.5 sacks and 2 interceptions . Cornerback Brian Kelly was also a big asset , leading the team with 8 interceptions . The Raiders win without Gruden ( edit ) Further information : 2002 Oakland Raiders season Despite the loss of Gruden in 2002 , the Raiders under their new coach Bill Callahan still managed to earn a share of the AFC 's best record at 11 -- 5 . The offense led the league in total passing yards ( 4,689 ) and ranked second in total yards gained ( 6,451 ) . Gannon had a Pro Bowl season , completing 418 out of 618 passes for 4,689 yards , 26 touchdowns , and with 10 interceptions . His 418 completions and his 10 games with over 300 passing yards were both NFL records . He also ran 50 times for 156 yards and 3 touchdowns . Rice , who was already the NFL 's all - time leader in nearly every receiving record after 17 seasons , had a Pro Bowl season for the 13th time in his career with 92 receptions for 1,211 yards and 7 touchdowns . Gannon 's other weapons in passing game were 15 - year veteran receiver Tim Brown ( 81 receptions for 930 yards and 2 touchdowns ) and young receiver Jerry Porter ( 51 receptions for 688 yards and 9 touchdowns ) . Multi-talented running back Charlie Garner was the team 's leading rusher with 962 yards and 7 touchdowns , while also leading all NFL running backs in receiving with 91 receptions for 941 yards and another 4 touchdowns . Running back Tyrone Wheatley was also a big contributor with 419 rushing yards and 71 receiving yards , while fullback Zack Crockett provided both of them with solid blocking and scored 8 touchdowns . Up front , their offensive line was led by 2 Pro Bowlers , guard Lincoln Kennedy and center Barret Robbins . The Raiders ' weakness was primarily on their defense , which ranked 25th in the league in passing yards allowed ( 3,787 ) and 12th in total yards ( 5,240 ) . But veteran Pro Bowl safety Rod Woodson recorded 8 interceptions ( which led the league ) for 225 yards and 2 touchdowns . Up front , their line was anchored by defensive tackle Rod Coleman , who led the team with 11 sacks . Behind him , the team had a solid veteran linebacker , Bill Romanowski , who was playing in his 5th Super Bowl ( after winning 2 championships with the San Francisco 49ers in Super Bowls XXIII and XXIV , and 2 while playing for the Denver Broncos in Super Bowls XXXII and XXXIII ) . Defensive back Tory James was also a big contributor with 4 interceptions . Playoffs ( edit ) Further information : 2002 -- 03 NFL playoffs The second - seeded Buccaneers defeated the fourth - seeded San Francisco 49ers , 31 -- 6 , and the top - seeded Philadelphia Eagles on the road , 27 -- 10 , in the playoffs , to make the Super Bowl for the first time in franchise history . Meanwhile , the top - seeded Raiders were victorious against the fourth - seeded New York Jets , 30 -- 10 , and the second - seeded Tennessee Titans , 41 -- 24 . The Raiders won against the Titans through Gannon 's pass - oriented offense . Super Bowl pre-game News ( edit ) The Raiders entered the game favored to win in their first Super Bowl in 19 years . They were also the first franchise to appear in the Super Bowl in four different decades ( 1960s , 1970s , 1980s , 2000s ; the 1990s was the only decade that they did n't appear in the Super Bowl ) . However , much of the media hype surrounded the Gruden trade prior to the season . This forced league commissioner Paul Tagliabue to issue a statement that he might ban all future trades for coaches involving draft choices because it might compromise the draft . A distraction for the Raiders was that starting center Barret Robbins went missing for most of the week leading up to the Super Bowl , and ended up in a San Diego hospital the night before the game after suffering a manic episode . Backup Adam Treu ( a former Pro Bowl - er ) replaced Robbins . Television and Entertainment ( edit ) The game was broadcast in the United States by ABC with Al Michaels handling the play - by - play duties and color commentator John Madden , who became the first person to announce Super Bowls on different networks in consecutive years , having called Super Bowl XXXVI on Fox and then moving to ABC after Pat Summerall retired . The NFC improved to 6 -- 0 on Super Bowls broadcast on ABC . Melissa Stark and Lynn Swann served as sideline reporters . Chris Berman from Disney - owned corporate sibling ESPN hosted all the events . Berman was joined by fellow ESPN analyst Steve Young , Baltimore Ravens head coach Brian Billick , and New York Giants defensive end Michael Strahan . The Super Bowl was the first of three major professional sports championship series ABC broadcast in 2003 , as they would also broadcast the Stanley Cup Finals and the NBA Finals . Both the Super Bowl and the Stanley Cup Finals were hosted by Berman ( who co-hosted the Stanley Cup Finals with John Saunders ) and took place in the state of California . The state of California had representation in both finals series . Gary Thorne , Bill Clement , and John Davidson mentioned all of these when they called the Stanley Cup Finals . Pre-game ceremonies ( edit ) Before the game , a show called `` Santana and Friends '' performed on the field . Carlos Santana was joined by Beyoncé and Michelle Branch and sang truncated versions of `` Oye Como Va '' , `` The Game of Love '' , and `` Foo Foo . '' ABC also aired a pre-game parking lot performance featuring Bonnie Raitt , Goo Goo Dolls and Michael Bublé prior to the Santana and Friends segment . In a nod to what the New England Patriots did the previous year in Super Bowl XXXVI , both teams were introduced as a team , rather than offensive and defensive starters , after highlights of their seasons were simulcast on the video boards in the stadium and on television . This has become a regular tradition starting with this Super Bowl . Celine Dion then sang `` God Bless America '' which is sung for the only time in the Super Bowl , and later the Dixie Chicks sang the national anthem , `` The Star - Spangled Banner '' . F / A-18 Super Hornets of the United States Navy performed a flyover . To honor the 30th anniversary of the 17 -- 0 undefeated , perfect season of the 1972 Miami Dolphins , the following members of that team appeared during the coin toss ceremony : Don Shula , Bob Griese , Larry Csonka , Larry Little , Jim Langer , Nick Buoniconti , Paul Warfield . Memorable television commercials that aired during the game included the `` Terry Tate : Office Linebacker '' Reebok ad and the Budweiser Zebra Referee . ADBOWL ranked FedEx 's `` Castaway '' as the best commercial of the year . Halftime show ( edit ) Shania Twain , No Doubt , and Sting were featured during the halftime show , which was sponsored by AT&T Wireless . Twain sang her hits `` Man ! I Feel Like a Woman ! '' and `` Up ! '' . No Doubt then sang their hit `` Just a Girl '' with lead singer Gwen Stefani ad - libbing lines like `` I 'm just a girl at the Super Bowl ! '' The show concluded with Sting performing `` Message in a Bottle '' , with Stefani joining in midway through . NBC provided counter-programming against the halftime show , airing a live segment of `` Weekend Update '' from the comedy -- variety show Saturday Night Live featuring Jimmy Fallon and Tina Fey . Postgame ceremonies ( edit ) Bon Jovi appeared as part of the post-game ceremonies , performing `` It 's My Life '' prior to the Vince Lombardi Trophy presentation and `` Everyday '' afterwards ( most of the latter performance was not shown on ABC because the network cut to commercials ) . Game Summary ( edit ) First quarter ( edit ) The Raiders had a great chance to score a touchdown early in the game after cornerback Charles Woodson intercepted Buccaneers quarterback Brad Johnson 's pass on the third play of the game and returned it 12 yards to the Tampa Bay 36 - yard line . However , six plays later , Tampa Bay defensive end Simeon Rice sacked Raiders quarterback Rich Gannon on third down , forcing Oakland to settle for kicker Sebastian Janikowski 's 40 - yard field goal to give them a 3 -- 0 lead . Buccaneers kick returner Aaron Stecker returned the ensuing kickoff 27 yards to the 29 - yard line , then appeared to fumble the ball . Although the officials initially ruled that the ball was recovered by Oakland 's Eric Johnson , the play was reviewed by instant replay and the fumble was overturned , and thus Tampa Bay retained possession . It showed that both of Stecker 's knees were down and the ball did n't come loose until it hit the ground . Gruden and Stecker appeared upset at having to use a challenge so early in a game , when they both believed Stecker was clearly down . On the first play of the drive , Brad Johnson completed an 11 - yard pass to wide receiver Joe Jurevicius . Johnson 's next 2 passes were incomplete , but he then completed a 23 - yard pass to Jurevicius on third down to advance the ball to the Oakland 37 - yard line . Running back Michael Pittman then rushed for a 23 - yard gain to the 13 - yard line . However , on the next 3 plays , the Raiders defense limited the Buccaneers to a pair of incompletions and a 1 - yard run . Argentine kicker Martín Gramática then made a 31 - yard field goal to tie the game , 3 -- 3 . Second quarter ( edit ) Later in the half , a 17 - yard punt return by Raiders defensive back Darrien Gordon gave Oakland the ball at their own 49 - yard line . Gannon then threw an 8 - yard pass to running back Charlie Garner to reach the Tampa Bay 43 - yard line . However , on third down , Buccaneers safety Dexter Jackson intercepted Gannon 's pass at the 40 - yard line and returned it 9 - yards to near midfield . Then nine plays after the turnover , Gramatica kicked his second field goal from 43 yards to give Tampa Bay a 6 -- 3 lead . Jackson intercepted another pass on the Raiders ' next drive and returned it 25 yards to Oakland 's 45 - yard line , making Jackson the first player ever to record two interceptions in the first half of the Super Bowl . However , the Buccaneers were unable to take advantage of the turnover and were forced to punt . Fortunately for Tampa Bay , they got a big assist from their punter Tom Tupa , who managed to pin Oakland all the way back at their own 11 - yard line with his punt . The Raiders could not move the ball either , losing 1 yard on 3 plays with their ensuing drive . Tampa Bay punt returner Karl Williams then returned Shane Lechler 's punt 25 yards , giving the Buccaneers great field position at Oakland 's 27 - yard line . Aided with Pittman 's gains of 6 and 19 yards , the Buccaneers scored their first touchdown on a 2 - yard run from fullback Mike Alstott , increasing their lead to 13 -- 3 . Then with 3 : 45 left in the half , Tampa Bay drove 77 yards , assisted by a pair of catches by Alstott for 28 total yards . Johnson finished the drive with a 5 - yard touchdown pass to wide receiver Keenan McCardell to give the Buccaneers a 20 -- 3 halftime lead . Third quarter ( edit ) Tampa Bay continued to dominate the game for most of the third quarter . The Buccaneers forced the Raiders to punt on the opening drive of the second half . Next , Tampa Bay marched 89 yards on a 14 - play drive that took 7 : 52 off the clock , and ended with Johnson 's 8 - yard touchdown pass to McCardell to increase their lead to 27 -- 3 . Then on the second play of Oakland 's ensuing drive , Buccaneers defensive back Dwight Smith intercepted Gannon 's pass and returned it 44 yards for a touchdown , making the score 34 -- 3 . After giving up 34 points , Oakland finally managed to drive 82 yards down the field and score on a 39 - yard touchdown pass from Gannon to wide receiver Jerry Porter . Although he was initially ruled as being out of bounds when he caught the ball , it was determined that Porter had both feet in the end zone . The two - point conversion failed , so the Raiders were still down 34 -- 9 . Fourth quarter ( edit ) The Raiders ' touchdown seemed to fire up their defense , who forced the Buccaneers to a fourth down on their ensuing possession . Oakland linebacker Tim Johnson then blocked Tupa 's punt , and linebacker Eric Johnson returned the ball 13 yards for a touchdown . Another two - point conversion for Oakland failed , but Tampa Bay 's lead was cut to 34 -- 15 . Tampa Bay responded by moving the ball to the Oakland 9 - yard line on their ensuing drive , featuring a 24 - yard run by Pittman , but they came up empty after Tupa fumbled the snap on a field goal attempt . A few plays later , Gannon threw a 48 - yard touchdown pass to wide receiver Jerry Rice with 6 : 06 left in the game , cutting the Raiders deficit to 34 -- 21 . The two - point conversion failed when Jerry Porter caught the ball but landed out of bounds . Though there was contact with a defender , the officials deemed the contact incidental rather than a force - out , and therefore that part of the play was non-reviewable . In an attempt to prevent a Raiders comeback , the Buccaneers managed to run the clock down to 2 : 44 on their ensuing drive before being forced to punt . Then on third and 18 from the Oakland 29 - yard line , Tampa Bay linebacker Derrick Brooks intercepted a pass from Gannon and returned it 44 yards for a touchdown , giving the Buccaneers a 41 -- 21 lead with only 1 : 18 left , and leading Buccaneers radio announcer Gene Deckerhoff to make his famous call of `` The dagger 's in , we 're gon na win the Super Bowl ! '' . A few plays later , with the Raiders now playing for pride , Dwight Smith intercepted a tipped pass and returned it 50 yards for a touchdown with only two seconds remaining . Gramatica kicked the extra point , and the Buccaneers were up 48 -- 21 . Raiders defensive tackle Chris Cooper returned Gramatica 's kickoff 6 yards before being tackled by Jack Golden , ending the game . The Buccaneers won their first - ever Super Bowl with a 48 - 21 victory . Gannon said after the game that his performance was `` nightmarish '' . Box score ( edit ) Super Bowl XXXVII : Tampa Bay Buccaneers 48 , Oakland Raiders 21 Total Raiders ( AFC ) 0 6 12 21 Buccaneers ( NFC ) 17 14 14 48 at Qualcomm Stadium , San Diego , California Date : January 26 , 2003 Game time : 3 : 26 p.m. PST Game weather : 81 ° F ( 27 ° C ) , sunny Super Bowl XXXVII Box Score ( hide ) Scoring summary Quarter Time Drive Team Scoring information Score Plays Yards TOP OAK TB 10 : 40 7 14 2 : 55 OAK 40 - yard field goal by Sebastian Janikowski 0 7 : 51 9 58 2 : 49 TB 31 - yard field goal by Martín Gramática 11 : 16 9 26 3 : 53 TB 43 - yard field goal by Martín Gramática 6 6 : 24 27 2 : 02 TB Mike Alstott 2 - yard touchdown run , Martín Gramática kick good 13 0 : 30 10 77 3 : 15 TB Keenan McCardell 5 - yard touchdown reception from Brad Johnson , Martín Gramática kick good 20 5 : 30 14 89 7 : 52 TB Keenan McCardell 8 - yard touchdown reception from B. Johnson , Martín Gramática kick good 27 4 : 47 -- -- -- TB Interception returned 44 yards for touchdown by Dwight Smith , Martín Gramática kick good 34 2 : 14 8 82 2 : 33 OAK Jerry Porter 39 - yard touchdown reception from Rich Gannon , 2 - point pass no good 9 34 14 : 16 -- -- -- OAK Eric Johnson 13 - yard punt block return for a touchdown , 2 - point pass no good 15 34 6 : 06 8 78 2 : 56 OAK Jerry Rice 48 - yard touchdown reception from Rich Gannon , 2 - point pass no good 21 34 1 : 18 -- -- -- TB Interception returned 44 yards for touchdown by Derrick Brooks , Martín Gramática kick good 21 41 0 : 02 -- -- -- TB Interception returned 50 yards for touchdown by Dwight Smith , Martín Gramática kick good 21 48 `` TOP '' = time of possession . For other American football terms , see Glossary of American football . 21 48 Statistical overview ( edit ) Tampa Bay dominated Oakland , outgaining them in total yards ( 365 to 269 ) , rushing yards ( 150 to 19 ) , first downs ( 24 to 11 ) , offensive plays ( 76 to 60 ) , and forced turnovers ( 5 to 1 ) . As many sports fans and writers predicted , Gruden 's prior knowledge of the Raiders was a major factor . The most damaging piece of evidence is NFL Films footage of Tampa Bay defensive back John Lynch telling his teammates during the game that almost all of the plays ran by Oakland 's offense were plays that Gruden ( who that week even played the part of `` Rich Gannon '' by playing QB with the scout - team offense ) specifically told them to look out for . Better still for the Buccaneers was that Oakland had n't changed their audible - calling signals that Gruden himself had installed , thus tipping off plays repeatedly . Johnson finished the game with 18 out of 34 completions for 215 yards and 2 touchdowns , with 1 interception , along with 10 rushing yards . Pittman was the top rusher of the game with 129 yards . Alstott was the game 's second leading rusher with 15 yards and a touchdown , and had 5 receptions for 43 yards . Wide receiver Keyshawn Johnson was the Buccaneers ' leading receiver with 6 catches for 69 yards . Smith recorded 2 interceptions , 94 return yards , and 2 touchdowns . He also added another 23 yards on a kickoff return . Gannon finished the game 24 out of 44 for 272 yards and 2 touchdowns , but was intercepted a Super Bowl record 5 times . Garner was their leading rusher , but with only 10 yards , and caught 7 passes for 51 yards . Rice was the Raiders ' leading receiver of the game with 5 catches for 77 yards and a touchdown . He became the first player to score touchdowns with two different teams in Super Bowls ( Ricky Proehl and Muhsin Muhammad have since joined him ) . Wide receiver Marcus Knight returned 8 kickoffs for 143 yards . Jerry Rice and Bill Romanowski joined Gene Upshaw as the only players to appear in Super Bowls in three different decades . Rice played in Super Bowls XXIII , XXIV , and XXIX . Romanowski played in Super Bowls XXIII , XXIV , XXXII , and XXXIII ; the Raiders ' loss prevented Romanowski from joining Charles Haley as the only NFL players at that time to earn 5 Super Bowl rings ( Haley was also with the 49ers for Super Bowls XXIII and XXIV , and later earned rings when the Dallas Cowboys won Super Bowls XXVII , XXVIII , and XXX ) . The Raiders became the first team to appear in Super Bowls under four different head coaches . John Rauch coached them in Super Bowl II , John Madden ( who himself called Super Bowl XXXVII on ABC ) , coached them in Super Bowl XI and Tom Flores coached them in Super Bowl XV and XVIII . The teams combined for the most second half points in a Super Bowl with 46 ( 28 for Tampa Bay and 18 for Oakland ) and the second most total points in a game with 69 , tying Dallas and Buffalo who combined for 69 points in Super Bowl XXVII . Final statistics ( edit ) Sources : NFL.com Super Bowl XXXVII , Super Bowl XXXVII Play Finder TB , Super Bowl XXXVII Play Finder Oak , Super Bowl XXXVII Play by Play Statistical comparison ( edit ) Oakland Raiders Tampa Bay Buccaneers First downs 11 24 First downs rushing 6 First downs passing 9 15 First downs penalty Third down efficiency 7 / 16 6 / 15 Fourth down efficiency 0 / 0 0 / 1 Net yards rushing 19 150 Rushing attempts 11 42 Yards per rush 1.7 3.6 Passing -- Completions - attempts 24 / 44 18 / 34 Times sacked - total yards 5 -- 22 0 - 0 Interceptions thrown 5 Net yards passing 250 215 Total net yards 269 365 Punt returns - total yards 3 -- 29 1 -- 25 Kickoff returns - total yards 9 -- 149 4 -- 90 Interceptions - total return yards 1 -- 12 5 -- 172 Punts - average yardage 5 -- 39.0 5 -- 31.0 Fumbles - lost 1 -- 0 1 -- 0 Penalties - yards 7 -- 51 5 -- 41 Time of possession 22 : 46 37 : 14 Turnovers 5 Individual leaders ( edit ) Raiders Passing C / ATT Yds TD INT Rating Rich Gannon 24 / 44 272 5 48.9 Raiders Rushing Car Yds TD LG Yds / Car Charlie Garner 7 10 0 1.43 Zack Crockett 6 0 3.00 Rich Gannon 0 1.00 Raiders Receiving Rec Yds TD LG Target Charlie Garner 7 51 0 9 11 Jerry Rice 5 77 48t 8 Doug Jolley 5 59 0 25 7 Jerry Porter 62 39t 9 Tim Brown 9 0 9 Jon Ritchie 7 0 7 Tyrone Wheatley 7 0 7 Marcus Knight 0 0 0 0 Buccaneers Passing C / ATT Yds TD INT Rating Brad Johnson 18 / 34 215 79.9 Buccaneers Rushing Car Yds TD LG Yds / Car Michael Pittman 29 124 0 24 4.28 Mike Alstott 10 15 5 1.50 Brad Johnson 10 0 10 10.00 Aaron Stecker 0 1.00 Tom Tupa 0 0 0 0.00 Buccaneers Receiving Rec Yds TD LG Target Keyshawn Johnson 6 69 0 18 11 Mike Alstott 5 43 0 16 8 Joe Jurevicius 78 0 33 Keenan McCardell 13 8t Ken Dilger 12 0 12 Rickey Dudley 0 0 0 0 Completions / attempts Carries Long gain Receptions Times targeted Starting lineups ( edit ) Source : Hall of Fame ‡ Oakland Position Position Tampa Bay Offense Tim Brown ‡ WR Keyshawn Johnson Barry Sims LT Roman Oben Frank Middleton LG Kerry Jenkins Adam Treu Jeff Christy Mo Collins RG Cosey Coleman Lincoln Kennedy RT Kenyatta Walker Doug Jolley TE Ken Dilger Jerry Rice ‡ WR Keenan McCardell Rich Gannon QB Brad Johnson Jerry Porter WR FB Mike Alstott Charlie Garner RB Michael Pittman Defense DeLawrence Grant DE LE Greg Spires Sam Adams DT Warren Sapp ‡ John Parrella DT NT Chuck Darby Regan Upshaw DE RE Simeon Rice Bill Romanowski LLB SLB Dwight Smith Napoleon Harris MLB Shelton Quarles Eric Barton RLB WLB Derrick Brooks ‡ Charles Woodson LCB Brian Kelly Tory James RCB Ronde Barber Anthony Dorsett SS John Lynch Rod Woodson ‡ FS Dexter Jackson Postgame riots ( edit ) In Oakland , after the Raiders ' loss , riots broke out on the streets of East Oakland . Twelve cars were set on fire and four hundred police officers had to be sent to the streets . Aftermath ( edit ) The Tampa Tribune published a book by several staff writers called Pewter Power , about the Buccaneers ' winning season . Both teams entered a period of decline after the Super Bowl . Neither made the playoffs the next season as Tampa Bay finished 7 -- 9 and Oakland finished 4 -- 12 . Furthermore , Tampa Bay finished 5 -- 11 in 2004 , becoming the first Super Bowl winning team to follow up with consecutive losing seasons . To date , the Buccaneers have yet to win another postseason game , while the Raiders went 14 seasons without having a winning season and / or qualifying the playoffs , and have also not won a playoff game since . Officials ( edit ) Referee : Bill Carollo # 63 second Super Bowl ( XXXI as side judge ) Umpire : Ed Coukart # 71 second Super Bowl ( originally alternate for XXXII , but entered game when Jim Quirk was injured ) Head Linesman : Dale Williams # 8 third Super Bowl ( XX , XXVI ) Line Judge : Mark Steinkerchner # 84 first Super Bowl Side Judge : Rick Patterson # 15 first Super Bowl Field Judge : Tom Sifferman # 118 first Super Bowl Back Judge : Don Carey # 126 first Super Bowl Replay Official : Rex Stuart Video Operator : Mike Wimmer Notes and references ( edit ) Jump up ^ DiNitto , Marcus ( January 25 , 2015 ) . `` Super Bowl Betting History -- Underdogs on Recent Roll '' . The Linemakers . Sporting News . Retrieved February 4 , 2015 . Jump up ^ `` Super Bowl History '' . Vegas Insider . Retrieved February 4 , 2015 . Jump up ^ `` Super Bowl Winners '' . NFL.com . Retrieved February 4 , 2015 . Jump up ^ `` Historical Super Bowl Nielsen TV Ratings , 1967 -- 2009 -- Ratings '' . TVbytheNumbers . Retrieved October 9 , 2012 . Jump up ^ `` mcubed.net : NFL : Super bowl scores sorted by margin of victory '' . mcubed.net . Retrieved February 3 , 2016 . Jump up ^ Martzke , Rudy ( January 27 , 2003 ) . `` Gruden Bowl keeps fans glued to TVs '' . USA Today . USATODAY.com . Jump up ^ White , Joseph ( October 16 , 1997 ) . `` 2003 Super Bowl to San Francisco ; Cleveland waits for team '' . Spartanburg Herald - Journal . p. 18 . Retrieved January 24 , 2017 -- via Google News . Jump up ^ `` New Orleans to host 2002 Super Bowl '' . Daily News . October 29 , 1998 . p. 8 . Retrieved January 24 , 2017 -- via Google News . Jump up ^ `` NFL -- Owners Meeting '' . The Orlando Sentinel . May 27 , 1999 . p. 38 . Retrieved January 24 , 2017 -- via Newspapers.com . ^ Jump up to : NHL on ABC : Game 7 of the 2003 Stanley Cup Finals ( television ) . ABC Sports . June 9 , 2003 . Thorne , Clement , and J.D. talked about Berman 's role in hosting both the Super Bowl and the Stanley Cup Finals on ABC in 2003 and about the role the state of California played during championship series during the Stanley Cup Finals , as Arrowhead Pond of Anaheim hosted the Stanley Cup Finals , and involved the Mighty Ducks of Anaheim ( now Anaheim Ducks ) taking on the New Jersey Devils . Jump up ^ `` Buccaneers get their first shot at the NFL treasure '' . Sydney Morning Herald . Associated Press . January 21 , 2003 . Retrieved August 27 , 2012 . Jump up ^ `` Gannon leads Raiders in rout of Jets '' . ESPN . Associated Press . January 12 , 2003 . Retrieved August 27 , 2012 . ^ Jump up to : Clayton , John . `` Raiders pass their way to San Diego '' . ESPN . Archived from the original on March 21 , 2008 . Jump up ^ Stroud , Rick ( January 17 , 2003 ) . `` NFL nixes draft picks for coaches '' . St. Petersburg Times . Retrieved August 27 , 2012 . Jump up ^ Taylor , Phil . `` When Barret Robbins disappeared before Super Bowl '' . SI.com . Retrieved 2016 - 11 - 30 . Jump up ^ `` Highlights of ABC 's pre - and postgame shows '' . ESPN . January 15 , 2003 . Retrieved August 27 , 2012 . Jump up ^ Mitchell , Fred ( January 27 , 2003 ) . `` In their fashion , Bucs fans laugh '' . Chicago Tribune . Retrieved August 27 , 2012 . Jump up ^ Vivinetto , Gina ( January 27 , 2003 ) . `` Super Bowl XXXVII : Superstars belt out favorites , or lip synch them '' . St. Petersburg Times . ^ Jump up to : George , Thomas ( January 27 , 2003 ) . `` Bucs steal the treasure '' . The New York Times . Retrieved August 27 , 2012 . ^ Jump up to : `` Tampa Bay Buccaneers 48 vs. Oakland Raiders 21 '' . pro-football - reference . Retrieved August 27 , 2012 . Jump up ^ Cunningham , Michael ; Skolnick , Ethan J. ( January 27 , 2003 ) . `` Treu Gets The Call In Robbins ' Absence '' . South Florida Sun - Sentinel . Retrieved August 27 , 2012 . ^ Jump up to : `` Bucs stop here -- with a Super Bowl title '' . USA Today . January 26 , 2003 . Retrieved August 27 , 2012 . Jump up ^ Pompei , Dan ( January 27 , 2003 ) . `` The best - laid plans : an inside look at how coach Jon Gruden and the Bucs prepared themselves to be Super Bowl champions '' . The Sporting News . Archived from the original on August 19 , 2003 . Jump up ^ `` Super Bowl XXXVII -- National Football League Game Summary '' ( PDF ) . National Football League . January 26 , 2003 . Retrieved January 8 , 2017 . Jump up ^ Martin , Glen ; Asimov , Nanette ; et al. ( January 27 , 2003 ) . `` Raider Rage : Oakland police no match for street mayhem '' . San Francisco Chronicle . p . A1 . Archived from the original on February 10 , 2003 . Super Bowl XXXVII : NFL Full Game on YouTube Super Bowl official website Play - by - play on USAToday.com 2006 NFL Record and Fact Book . Time Inc . Home Entertainment . ISBN 1 - 933405 - 32 - 5 . The Sporting News : History of the Super Bowl ( Last accessed December 4 , 2005 ) http://www.pro-football-reference.com -- Large online database of NFL data and statistics Super Bowl play - by - plays from USA Today ( Last accessed September 28 , 2005 ) All - Time Super Bowl Odds from The Sports Network ( Last accessed October 16 , 2005 ) Super Bowl NFL NFC Championship AFC Championship Football Games 1960s I ( 1967 ) II ( 1968 ) III ( 1969 ) 1970s IV ( 1970 ) V ( 1971 ) VI ( 1972 ) VII ( 1973 ) VIII ( 1974 ) IX ( 1975 ) X ( 1976 ) XI ( 1977 ) XII ( 1978 ) XIII ( 1979 ) 1980s XIV ( 1980 ) XV ( 1981 ) XVI ( 1982 ) XVII ( 1983 ) XVIII ( 1984 ) XIX ( 1985 ) XX ( 1986 ) XXI ( 1987 ) XXII ( 1988 ) XXIII ( 1989 ) 1990s XXIV ( 1990 ) XXV ( 1991 ) XXVI ( 1992 ) XXVII ( 1993 ) XXVIII ( 1994 ) XXIX ( 1995 ) XXX ( 1996 ) XXXI ( 1997 ) XXXII ( 1998 ) XXXIII ( 1999 ) 2000s XXXIV ( 2000 ) XXXV ( 2001 ) XXXVI ( 2002 ) XXXVII ( 2003 ) XXXVIII ( 2004 ) XXXIX ( 2005 ) XL ( 2006 ) XLI ( 2007 ) XLII ( 2008 ) XLIII ( 2009 ) 2010s XLIV ( 2010 ) XLV ( 2011 ) XLVI ( 2012 ) XLVII ( 2013 ) XLVIII ( 2014 ) XLIX ( 2015 ) 50 ( 2016 ) LI ( 2017 ) LII ( 2018 ) LIII ( 2019 ) 2020s LIV ( 2020 ) LV ( 2021 ) LVI ( 2022 ) People Champions Pre-Super Bowl NFL champions Head coaches Active head coach history Quarterbacks Officials Awards , trophies , records Super Bowl ring Vince Lombardi Trophy Most Valuable Players Records Broadcast and production National anthem Halftime Commercials USA Today Ad Meter Adbowl List Broadcast Network broadcasters Counterprogramming Lead - out programming Television ratings Super Bowl Sunday Curse Tampa Bay Buccaneers Super Bowl XXXVII champions 7 Martín Gramática 9 Tom Tupa 10 Shaun King 11 Rob Johnson 14 Brad Johnson 19 Keyshawn Johnson 20 Ronde Barber 23 Jermaine Phillips 25 Brian Kelly 26 Dwight Smith 27 Aaron Stecker 30 Darian Barnes 31 Tim Wansley 32 Michael Pittman 34 Dexter Jackson ( MVP ) 35 Corey Ivy 36 Travis Stephens 38 John Howell 40 Mike Alstott 41 Daniel Wilcox 43 Jameel Cook 45 Mike Solwold 47 John Lynch 51 Alshermond Singleton 52 Nate Webster 53 Shelton Quarles 54 Idris Price 55 Derrick Brooks 56 Ryan Nece 58 Jack Golden 59 Justin Smith 60 Cosey Coleman 62 Jeff Christy 64 Dan Goodspeed 65 Russ Hochstein 66 Ryan Benjamin 67 Kenyatta Walker 68 Morris Unutoa 71 Kerry Jenkins 72 Roman Oben 74 Cornell Green 75 Lomas Brown 77 Todd Washington 80 Todd Yoder 81 Charles Lee 81 Marco Battaglia 83 Joe Jurevicius 84 Reggie Barlow 85 Ken Dilger 86 Karl Williams 87 Keenan McCardell 88 Rickey Dudley 89 Casey Crawford 90 Buck Gurley 91 Chuck Darby 92 Anthony McFarland 93 DeVone Claybrooks 94 Greg Spires 95 Ron Warner 96 Ellis Wyms 97 Simeon Rice 98 Corey Smith 99 Warren Sapp -- Onome Ojo -- T.T. Toliver Head coach : Jon Gruden Coaches : Joe Barry Jeremy Bates Richard Bisaccia Michael Christianson Jay Gruden Monte Kiffin Richard Mann Rod Marinelli Raheem Morris Bill Muir Johnny Parker Stan Parrish Mike Tomlin Art Valero Kirby Wilson Tampa Bay Buccaneers Founded in 1976 Based and headquartered in Tampa , Florida Franchise Franchise Seasons History Coaches Players Expansion draft First - round draft picks Draft history Starting quarterbacks Broadcasters Stadiums Tampa Stadium Raymond James Stadium Culture and lore Hugh Culverhouse Malcolm Glazer Tampa 2 Captain Fear Cheerleaders Snow Bowl A Triumph of the Heart : The Ricky Bell Story Rivalries Carolina Panthers New Orleans Saints Miami Dolphins Playoff appearances ( 10 ) 1979 1981 1982 1997 1999 2000 2001 2002 2005 2007 Division championships ( 6 ) 1979 1981 1999 2002 2005 2007 Conference championships ( 1 ) 2002 League championships ( 1 ) 2002 ( XXXVII ) Hall of Fame members Lee Roy Selmon Steve Young Randall McDaniel Warren Sapp Derrick Brooks Tim Brown Ron Wolf Retired numbers 55 63 99 Current league affiliations League : National Football League Conference : National Football Conference Division : South Division Seasons ( 42 ) 1976 1977 1978 1979 1980 1981 1982 1984 1985 1986 1988 1989 1990 1991 1992 1993 1994 1995 1997 1998 1999 2000 2001 2002 2003 2005 2006 2007 2008 2009 2011 2012 2013 2014 2015 2016 2017 Championship seasons in bold Oakland Raiders Founded in 1960 Played in Los Angeles ( 1982 -- 94 ) Based in Oakland , California Headquartered in Alameda , California Franchise History in Los Angeles relocation to Las Vegas Seasons Players First - round draft picks Starting quarterbacks Head coaches Stadiums Kezar Stadium Candlestick Park Frank Youell Field Oakland -- Alameda County Coliseum Los Angeles Memorial Coliseum Las Vegas Stadium Key personnel Owner / CEO : Mark Davis President : Marc Badain General manager : Reggie McKenzie Head coach : Jon Gruden Culture Oakland Raiderettes Raider Nation The Autumn Wind Mount Davis Ricky 's Sports Theatre and Grill Straight Outta L.A. Lore Heidi Game Immaculate Reception The Sea of Hands Ghost to the Post Holy Roller Red Right 88 Tuck Rule Game Rivalries Denver Broncos Kansas City Chiefs Los Angeles Chargers Pittsburgh Steelers Media Broadcasters Television : NBC Sports California NBC Sports Bay Area KTVU KVVU Radio : KGMZ KBLX KUFX KCYE KDWN Other : Compass Media Networks The Raider Cast Personalities : Bill King Greg Papa J.T. the Brick Playoff appearances ( 22 ) 1967 1968 1969 1970 1972 1973 1976 1977 1980 1982 1984 1985 1990 1991 1993 2000 2001 2002 2016 Division championships ( 15 ) 1967 1968 1969 1970 1972 1973 1976 1985 1990 2000 2001 2002 Conference championships ( 4 ) 1976 1980 2002 League championships ( 3 ) 1976 ( XI ) 1980 ( XV ) 1983 ( XVIII ) does not include 1967 AFL championship Current league affiliations League : National Football League ( 1970 -- present ) Conference : American Football Conference Division : West Division Former league affiliation League : American Football League ( 1960 -- 1969 ) Seasons ( 58 ) 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1976 1977 1978 1979 1980 1981 1982 1984 1985 1986 1988 1989 1990 1991 1992 1993 1994 1995 1997 1998 1999 2000 2001 2002 2003 2005 2006 2007 2008 2009 2011 2012 2013 2014 2015 2016 2017 Championship seasons in bold ( hide ) 2002 NFL season AFC East North South West East North South West NFC Buffalo Baltimore Houston Denver Dallas Chicago Atlanta Arizona Miami Cincinnati Indianapolis Kansas City NY Giants Detroit Carolina St. Louis New England Cleveland Jacksonville Oakland Philadelphia Green Bay New Orleans San Francisco NY Jets Pittsburgh Tennessee San Diego Washington Minnesota Tampa Bay Seattle 2002 NFL Draft NFL playoffs Pro Bowl Super Bowl XXXVII National Football League Championship Games ( 1933 -- present ) NFL Championship Game ( 1933 -- 1969 ) 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 AFL Championship Game ( 1960 -- 1969 ) 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 AFL - NFL World Championship Games ( 1966 -- 1969 ) 1966 ( I ) 1967 ( II ) 1968 ( III ) 1969 ( IV ) Super Bowl ( 1970 -- present ) 1970 ( V ) 1971 ( VI ) 1972 ( VII ) 1973 ( VIII ) 1974 ( IX ) 1975 ( X ) 1976 ( XI ) 1977 ( XII ) 1978 ( XIII ) 1979 ( XIV ) 1980 ( XV ) 1981 ( XVI ) 1982 ( XVII ) 1983 ( XVIII ) 1984 ( XIX ) 1985 ( XX ) 1986 ( XXI ) 1987 ( XXII ) 1988 ( XXIII ) 1989 ( XXIV ) 1990 ( XXV ) 1991 ( XXVI ) 1992 ( XXVII ) 1993 ( XXVIII ) 1994 ( XXIX ) 1995 ( XXX ) 1996 ( XXXI ) 1997 ( XXXII ) 1998 ( XXXIII ) 1999 ( XXXIV ) 2000 ( XXXV ) 2001 ( XXXVI ) 2002 ( XXXVII ) 2003 ( XXXVIII ) 2004 ( XXXIX ) 2005 ( XL ) 2006 ( XLI ) 2007 ( XLII ) 2008 ( XLIII ) 2009 ( XLIV ) 2010 ( XLV ) 2011 ( XLVI ) 2012 ( XLVII ) 2013 ( XLVIII ) 2014 ( XLIX ) 2015 ( 50 ) 2016 ( LI ) 2017 ( LII ) 1921 APFA de facto championship game 1925 NFL Championship controversy 1932 NFL Playoff Game NFL Championship broadcasters AFL Championship broadcasters Super Bowl champions Super Bowl Most Valuable Players Super Bowl records Super Bowl broadcasters Super Bowl officials Super Bowl halftime Super Bowl commercials Pre-Super Bowl NFL champions NFL playoffs ( Results ) AFL playoffs 1 -- From 1966 to 1969 , the first four Super Bowls were `` World Championship '' games played between two independent professional football leagues , AFL and NFL , and when the league merged in 1970 the Super Bowl became the NFL Championship Game . 2 -- Dates in the list denote the season , not the calendar year in which the championship game was played . 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Question: who was the buccaneers qb when they won the superbowl


Independence ( probability theory ) - wikipedia Independence ( probability theory ) Jump to : navigation , search Part of a series on Statistics Probability theory Probability axioms Probability space Sample space Elementary event Event Random variable Probability measure Complementary event Joint probability Marginal probability Conditional probability Independence Conditional independence Law of total probability Law of large numbers Bayes ' theorem Boole 's inequality Venn diagram Tree diagram In probability theory , two events are independent , statistically independent , or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other . Similarly , two random variables are independent if the realization of one does not affect the probability distribution of the other . The concept of independence extends to dealing with collections of more than two events or random variables , in which case the events are pairwise independent if each pair are independent of each other , and the events are mutually independent if each event is independent of each other combination of events . Contents ( hide ) 1 Definition 1.1 For events 1.1. 1 Two events 1.1. 2 More than two events 1.2 For random variables 1.2. 1 Two random variables 1.2. 2 More than two random variables 1.2. 3 Conditional independence 1.3 Independent σ - algebras 2 Properties 2.1 Self - independence 2.2 Expectation and covariance 2.3 Characteristic function 3 Examples 3.1 Rolling dice 3.2 Drawing cards 3.3 Pairwise and mutual independence 3.4 Mutual independence 4 See also 5 References Definition ( edit ) For events ( edit ) Two events ( edit ) Two events A and B are independent ( often written as A ⊥ B ( \ displaystyle A \ perp B ) or A ⊥ ⊥ B ( \ displaystyle A \ perp \ ! \ ! \ ! \ perp B ) ) if their joint probability equals the product of their probabilities : P ( A ∩ B ) = P ( A ) P ( B ) ( \ displaystyle \ mathrm ( P ) ( A \ cap B ) = \ mathrm ( P ) ( A ) \ mathrm ( P ) ( B ) ) . Why this defines independence is made clear by rewriting with conditional probabilities : P ( A ∩ B ) = P ( A ) P ( B ) ⇔ P ( A ) = P ( A ∩ B ) P ( B ) = P ( A ∣ B ) ( \ displaystyle \ mathrm ( P ) ( A \ cap B ) = \ mathrm ( P ) ( A ) \ mathrm ( P ) ( B ) \ Leftrightarrow \ mathrm ( P ) ( A ) = ( \ frac ( \ mathrm ( P ) ( A \ cap B ) ) ( \ mathrm ( P ) ( B ) ) ) = \ mathrm ( P ) ( A \ mid B ) ) . and similarly P ( A ∩ B ) = P ( A ) P ( B ) ⇔ P ( B ) = P ( B ∣ A ) ( \ displaystyle \ mathrm ( P ) ( A \ cap B ) = \ mathrm ( P ) ( A ) \ mathrm ( P ) ( B ) \ Leftrightarrow \ mathrm ( P ) ( B ) = \ mathrm ( P ) ( B \ mid A ) ) . Thus , the occurrence of B does not affect the probability of A , and vice versa . Although the derived expressions may seem more intuitive , they are not the preferred definition , as the conditional probabilities may be undefined if P ( A ) or P ( B ) are 0 . Furthermore , the preferred definition makes clear by symmetry that when A is independent of B , B is also independent of A . More than two events ( edit ) A finite set of events ( A i ) i = 1 n ( \ displaystyle \ ( A_ ( i ) \ ) _ ( i = 1 ) ^ ( n ) ) is pairwise independent if every pair of events is independent -- that is , if and only if for all distinct pairs of indices m , k , P ( A m ∩ A k ) = P ( A m ) P ( A k ) . ( \ displaystyle \ mathrm ( P ) ( A_ ( m ) \ cap A_ ( k ) ) = \ mathrm ( P ) ( A_ ( m ) ) \ mathrm ( P ) ( A_ ( k ) ) . ) A finite set of events is mutually independent if every event is independent of any intersection of the other events -- that is , if and only if for every k - element subset of ( A i ) i = 1 n ( \ displaystyle \ ( A_ ( i ) \ ) _ ( i = 1 ) ^ ( n ) ) , P ( ⋂ i = 1 k A i ) = ∏ i = 1 k P ( A i ) . ( \ displaystyle \ mathrm ( P ) \ left ( \ bigcap _ ( i = 1 ) ^ ( k ) A_ ( i ) \ right ) = \ prod _ ( i = 1 ) ^ ( k ) \ mathrm ( P ) ( A_ ( i ) ) . ) This is called the multiplication rule for independent events . Note that it is not a single condition involving only the product of all the probabilities of all single events ( see below for a counterexample ) ; it must hold true for all subsets of events . For more than two events , a mutually independent set of events is ( by definition ) pairwise independent ; but the converse is not necessarily true ( see below for a counterexample ) . For random variables ( edit ) Two random variables ( edit ) Two random variables X and Y are independent if and only if ( iff ) the elements of the π - system generated by them are independent ; that is to say , for every a and b , the events ( X ≤ a ) and ( Y ≤ b ) are independent events ( as defined above ) . That is , X and Y with cumulative distribution functions F X ( x ) ( \ displaystyle F_ ( X ) ( x ) ) and F Y ( y ) ( \ displaystyle F_ ( Y ) ( y ) ) , and probability densities f X ( x ) ( \ displaystyle f_ ( X ) ( x ) ) and f Y ( y ) ( \ displaystyle f_ ( Y ) ( y ) ) , are independent iff the combined random variable ( X , Y ) has a joint cumulative distribution function F X , Y ( x , y ) = F X ( x ) F Y ( y ) , ( \ displaystyle F_ ( X , Y ) ( x , y ) = F_ ( X ) ( x ) F_ ( Y ) ( y ) , ) or equivalently , if the joint density exists , f X , Y ( x , y ) = f X ( x ) f Y ( y ) . ( \ displaystyle f_ ( X , Y ) ( x , y ) = f_ ( X ) ( x ) f_ ( Y ) ( y ) . ) More than two random variables ( edit ) A set of random variables is pairwise independent if and only if every pair of random variables is independent . Even if the set of random variables is pairwise independent , it is not necessarily mutually independent as defined next . A set of random variables is mutually independent if and only if for any finite subset X 1 , ... , X n ( \ displaystyle X_ ( 1 ) , \ ldots , X_ ( n ) ) and any finite sequence of numbers a 1 , ... , a n ( \ displaystyle a_ ( 1 ) , \ ldots , a_ ( n ) ) , the events ( X 1 ≤ a 1 ) , ... , ( X n ≤ a n ) ( \ displaystyle \ ( X_ ( 1 ) \ leq a_ ( 1 ) \ ) , \ ldots , \ ( X_ ( n ) \ leq a_ ( n ) \ ) ) are mutually independent events ( as defined above ) . The measure - theoretically inclined may prefer to substitute events ( X ∈ A ) for events ( X ≤ a ) in the above definition , where A is any Borel set . That definition is exactly equivalent to the one above when the values of the random variables are real numbers . It has the advantage of working also for complex - valued random variables or for random variables taking values in any measurable space ( which includes topological spaces endowed by appropriate σ - algebras ) . Conditional independence ( edit ) Main article : Conditional independence Intuitively , two random variables X and Y are conditionally independent given Z if , once Z is known , the value of Y does not add any additional information about X . For instance , two measurements X and Y of the same underlying quantity Z are not independent , but they are conditionally independent given Z ( unless the errors in the two measurements are somehow connected ) . The formal definition of conditional independence is based on the idea of conditional distributions . If X , Y , and Z are discrete random variables , then we define X and Y to be conditionally independent given Z if P ( X ≤ x , Y ≤ y Z = z ) = P ( X ≤ x Z = z ) ⋅ P ( Y ≤ y Z = z ) ( \ displaystyle \ mathrm ( P ) ( X \ leq x , Y \ leq y \ ; \ ; Z = z ) = \ mathrm ( P ) ( X \ leq x \ ; \ ; Z = z ) \ cdot \ mathrm ( P ) ( Y \ leq y \ ; \ ; Z = z ) ) for all x , y and z such that P ( Z = z ) > 0 . On the other hand , if the random variables are continuous and have a joint probability density function p , then X and Y are conditionally independent given Z if p X Y Z ( x , y z ) = p X Z ( x z ) ⋅ p Y Z ( y z ) ( \ displaystyle p_ ( XY Z ) ( x , y z ) = p_ ( X Z ) ( x z ) \ cdot p_ ( Y Z ) ( y z ) ) for all real numbers x , y and z such that p ( z ) > 0 . If discrete X and Y are conditionally independent given Z , then P ( X = x Y = y , Z = z ) = P ( X = x Z = z ) ( \ displaystyle \ mathrm ( P ) ( X = x Y = y , Z = z ) = \ mathrm ( P ) ( X = x Z = z ) ) for any x , y and z with P ( Z = z ) > 0 . That is , the conditional distribution for X given Y and Z is the same as that given Z alone . A similar equation holds for the conditional probability density functions in the continuous case . Independence can be seen as a special kind of conditional independence , since probability can be seen as a kind of conditional probability given no events . Independent σ - algebras ( edit ) The definitions above are both generalized by the following definition of independence for σ - algebras . Let ( Ω , Σ , P ) ( \ displaystyle ( \ Omega , \ Sigma , \ mathrm ( P ) ) ) be a probability space and let A ( \ displaystyle ( \ mathcal ( A ) ) ) and B ( \ displaystyle ( \ mathcal ( B ) ) ) be two sub-σ - algebras of Σ ( \ displaystyle \ Sigma ) . A ( \ displaystyle ( \ mathcal ( A ) ) ) and B ( \ displaystyle ( \ mathcal ( B ) ) ) are said to be independent if , whenever A ∈ A ( \ displaystyle A \ in ( \ mathcal ( A ) ) ) and B ∈ B ( \ displaystyle B \ in ( \ mathcal ( B ) ) ) , P ( A ∩ B ) = P ( A ) P ( B ) . ( \ displaystyle \ mathrm ( P ) ( A \ cap B ) = \ mathrm ( P ) ( A ) \ mathrm ( P ) ( B ) . ) Likewise , a finite family of σ - algebras ( τ i ) i ∈ I ( \ displaystyle ( \ tau _ ( i ) ) _ ( i \ in I ) ) , where I ( \ displaystyle I ) is an index set , is said to be independent if and only if ∀ ( A i ) i ∈ I ∈ ∏ i ∈ I τ i : P ( ⋂ i ∈ I A i ) = ∏ i ∈ I P ( A i ) ( \ displaystyle \ forall \ left ( A_ ( i ) \ right ) _ ( i \ in I ) \ in \ prod \ nolimits _ ( i \ in I ) \ tau _ ( i ) \ :\ \ mathrm ( P ) \ left ( \ bigcap \ nolimits _ ( i \ in I ) A_ ( i ) \ right ) = \ prod \ nolimits _ ( i \ in I ) \ mathrm ( P ) \ left ( A_ ( i ) \ right ) ) and an infinite family of σ - algebras is said to be independent if all its finite subfamilies are independent . The new definition relates to the previous ones very directly : Two events are independent ( in the old sense ) if and only if the σ - algebras that they generate are independent ( in the new sense ) . The σ - algebra generated by an event E ∈ Σ ( \ displaystyle E \ in \ Sigma ) is , by definition , σ ( ( E ) ) = ( ∅ , E , Ω ∖ E , Ω ) . ( \ displaystyle \ sigma ( \ ( E \ ) ) = \ ( \ emptyset , E , \ Omega \ setminus E , \ Omega \ ) . ) Two random variables X and Y defined over Ω are independent ( in the old sense ) if and only if the σ - algebras that they generate are independent ( in the new sense ) . The σ - algebra generated by a random variable X taking values in some measurable space S consists , by definition , of all subsets of Ω of the form X ( U ) , where U is any measurable subset of S . Using this definition , it is easy to show that if X and Y are random variables and Y is constant , then X and Y are independent , since the σ - algebra generated by a constant random variable is the trivial σ - algebra ( ∅ , Ω ) . Probability zero events can not affect independence so independence also holds if Y is only Pr - almost surely constant . Properties ( edit ) Self - independence ( edit ) Note that an event is independent of itself if and only if P ( A ) = P ( A ∩ A ) = P ( A ) ⋅ P ( A ) ⇔ P ( A ) = 0 or 1 ( \ displaystyle \ mathrm ( P ) ( A ) = \ mathrm ( P ) ( A \ cap A ) = \ mathrm ( P ) ( A ) \ cdot \ mathrm ( P ) ( A ) \ Leftrightarrow \ mathrm ( P ) ( A ) = 0 ( \ text ( or ) ) 1 ) . Thus an event is independent of itself if and only if it almost surely occurs or its complement almost surely occurs . Expectation and covariance ( edit ) If X and Y are independent , then the expectation operator E has the property E ( X Y ) = E ( X ) E ( Y ) , ( \ displaystyle E ( XY ) = E ( X ) E ( Y ) , ) and the covariance cov ( X , Y ) is zero , since we have cov ( X , Y ) = E ( X Y ) − E ( X ) E ( Y ) . ( \ displaystyle ( \ text ( cov ) ) ( X , Y ) = E ( XY ) - E ( X ) E ( Y ) . ) ( The converse of these , i.e. the proposition that if two random variables have a covariance of 0 they must be independent , is not true . See uncorrelated . ) Characteristic function ( edit ) Two random variables X and Y are independent if and only if the characteristic function of the random vector ( X , Y ) satisfies φ ( X , Y ) ( t , s ) = φ X ( t ) ⋅ φ Y ( s ) . ( \ displaystyle \ varphi _ ( ( X , Y ) ) ( t , s ) = \ varphi _ ( X ) ( t ) \ cdot \ varphi _ ( Y ) ( s ) . ) In particular the characteristic function of their sum is the product of their marginal characteristic functions : φ X + Y ( t ) = φ X ( t ) ⋅ φ Y ( t ) , ( \ displaystyle \ varphi _ ( X + Y ) ( t ) = \ varphi _ ( X ) ( t ) \ cdot \ varphi _ ( Y ) ( t ) , ) though the reverse implication is not true . Random variables that satisfy the latter condition are called subindependent . Examples ( edit ) Rolling dice ( edit ) The event of getting a 6 the first time a die is rolled and the event of getting a 6 the second time are independent . By contrast , the event of getting a 6 the first time a die is rolled and the event that the sum of the numbers seen on the first and second trials is 8 are not independent . Drawing cards ( edit ) If two cards are drawn with replacement from a deck of cards , the event of drawing a red card on the first trial and that of drawing a red card on the second trial are independent . By contrast , if two cards are drawn without replacement from a deck of cards , the event of drawing a red card on the first trial and that of drawing a red card on the second trial are not independent , because a deck that has had a red card removed has proportionately fewer red cards . Pairwise and mutual independence ( edit ) Pairwise independent , but not mutually independent , events . Mutually independent events . Consider the two probability spaces shown . In both cases , P ( A ) = P ( B ) = 1 / 2 and P ( C ) = 1 / 4 . The random variables in the first space are pairwise independent because P ( A B ) = P ( A C ) = 1 / 2 = P ( A ) , P ( B A ) = P ( B C ) = 1 / 2 = P ( B ) , and P ( C A ) = P ( C B ) = 1 / 4 = P ( C ) ; but the three random variables are not mutually independent . The random variables in the second space are both pairwise independent and mutually independent . To illustrate the difference , consider conditioning on two events . In the pairwise independent case , although any one event is independent of each of the other two individually , it is not independent of the intersection of the other two : P ( A B C ) = 4 40 4 40 + 1 40 = 4 5 ≠ P ( A ) ( \ displaystyle \ mathrm ( P ) ( A BC ) = ( \ frac ( \ frac ( 4 ) ( 40 ) ) ( ( \ frac ( 4 ) ( 40 ) ) + ( \ frac ( 1 ) ( 40 ) ) ) ) = ( \ tfrac ( 4 ) ( 5 ) ) \ neq \ mathrm ( P ) ( A ) ) P ( B A C ) = 4 40 4 40 + 1 40 = 4 5 ≠ P ( B ) ( \ displaystyle \ mathrm ( P ) ( B AC ) = ( \ frac ( \ frac ( 4 ) ( 40 ) ) ( ( \ frac ( 4 ) ( 40 ) ) + ( \ frac ( 1 ) ( 40 ) ) ) ) = ( \ tfrac ( 4 ) ( 5 ) ) \ neq \ mathrm ( P ) ( B ) ) P ( C A B ) = 4 40 4 40 + 6 40 = 2 5 ≠ P ( C ) ( \ displaystyle \ mathrm ( P ) ( C AB ) = ( \ frac ( \ frac ( 4 ) ( 40 ) ) ( ( \ frac ( 4 ) ( 40 ) ) + ( \ frac ( 6 ) ( 40 ) ) ) ) = ( \ tfrac ( 2 ) ( 5 ) ) \ neq \ mathrm ( P ) ( C ) ) In the mutually independent case , however , P ( A B C ) = 1 16 1 16 + 1 16 = 1 2 = P ( A ) ( \ displaystyle \ mathrm ( P ) ( A BC ) = ( \ frac ( \ frac ( 1 ) ( 16 ) ) ( ( \ frac ( 1 ) ( 16 ) ) + ( \ frac ( 1 ) ( 16 ) ) ) ) = ( \ tfrac ( 1 ) ( 2 ) ) = \ mathrm ( P ) ( A ) ) P ( B A C ) = 1 16 1 16 + 1 16 = 1 2 = P ( B ) ( \ displaystyle \ mathrm ( P ) ( B AC ) = ( \ frac ( \ frac ( 1 ) ( 16 ) ) ( ( \ frac ( 1 ) ( 16 ) ) + ( \ frac ( 1 ) ( 16 ) ) ) ) = ( \ tfrac ( 1 ) ( 2 ) ) = \ mathrm ( P ) ( B ) ) P ( C A B ) = 1 16 1 16 + 3 16 = 1 4 = P ( C ) ( \ displaystyle \ mathrm ( P ) ( C AB ) = ( \ frac ( \ frac ( 1 ) ( 16 ) ) ( ( \ frac ( 1 ) ( 16 ) ) + ( \ frac ( 3 ) ( 16 ) ) ) ) = ( \ tfrac ( 1 ) ( 4 ) ) = \ mathrm ( P ) ( C ) ) Mutual independence ( edit ) It is possible to create a three - event example in which P ( A ∩ B ∩ C ) = P ( A ) P ( B ) P ( C ) , ( \ displaystyle \ mathrm ( P ) ( A \ cap B \ cap C ) = \ mathrm ( P ) ( A ) \ mathrm ( P ) ( B ) \ mathrm ( P ) ( C ) , ) and yet no two of the three events are pairwise independent ( and hence the set of events are not mutually independent ) . This example shows that mutual independence involves requirements on the products of probabilities of all combinations of events , not just the single events as in this example . See also ( edit ) Copula ( statistics ) Independent and identically distributed random variables Mutually exclusive events Subindependence Linear dependence between random variables Conditional independence Normally distributed and uncorrelated does not imply independent Mean dependence References ( edit ) Jump up ^ Russell , Stuart ; Norvig , Peter ( 2002 ) . Artificial Intelligence : A Modern Approach . Prentice Hall . p. 478 . ISBN 0 - 13 - 790395 - 2 . ^ Jump up to : Feller , W ( 1971 ) . `` Stochastic Independence '' . An Introduction to Probability Theory and Its Applications . Wiley . Jump up ^ George , Glyn , `` Testing for the independence of three events , '' Mathematical Gazette 88 , November 2004 , 568 . PDF Retrieved from `` https://en.wikipedia.org/w/index.php?title=Independence_(probability_theory)&oldid=799275720 '' Categories : Experiment ( probability theory ) Independence ( probability theory ) Talk Contents About Wikipedia Català Deutsch Español Esperanto Euskara فارسی Français 한국어 Italiano עברית Bahasa Melayu Nederlands 日本 語 Polski Português Русский Simple English Slovenščina Basa Sunda Suomi Svenska ไทย Türkçe Українська اردو Tiếng Việt 中文 Edit links This page was last edited on 6 September 2017 , at 18 : 43 . Text is available under the Creative Commons Attribution - ShareAlike License ; additional terms may apply . By using this site , you agree to the Terms of Use and Privacy Policy . Wikipedia ® is a registered trademark of the Wikimedia Foundation , Inc. , a non-profit organization . About Wikipedia

Question: when are two events said to be independent


Defensive three - second violation - Wikipedia Defensive three - second violation Jump to : navigation , search A defensive three - second violation , also known as illegal defense , is a basketball rules infraction in the National Basketball Association ( NBA ) introduced in the 2001 -- 2002 season . It is assessed when a member of the defending team spends more than three seconds in the free throw lane ( also known as the 16 - foot lane , or colloquially as `` in the paint '' ) while not actively guarding an opponent . To be considered actively guarding , a defender must be within arm 's length of an opponent and in a guarding position . A three - second count is suspended if : a player is in the act of shooting there is a loss of team control the defender is actively guarding an opponent the defender clears the painted area it is imminent the defender will become legal In addition , a player guarding an opponent with the ball may be in the paint without actively guarding the opponent . The team committing a defensive three - second violation is assessed a team technical foul . The offense receives one free throw and retains possession of the ball . Prior to the 2001 -- 2002 NBA season , any form of zone defense was considered an illegal defense violation and resulted in a warning on the first violation and then a technical foul for any subsequent violations . However , the defensive three - second violation makes it difficult for NBA defenses to play zone , since zone defenses usually position a player in the middle of the key to stop penetration . The Philippine Basketball Association used to follow the illegal defense rule until the 2003 PBA season when it was abolished . The high school game does not use this rule , nor does European basketball . The WNBA started using it in 2013 . References ( edit ) Jump up ^ NBA Official Rules ( 2009 - 2010 ) Rule 10 , Section VII , B. Retrieved July 25 , 2010 Jump up ^ NBA Official Rules ( 2009 - 2010 ) Rule 10 , Section VII , D. Retrieved July 25 , 2010 Jump up ^ NBA Official Rules ( 2009 - 2010 ) Rule 10 , Section VII , E. Retrieved July 25 , 2010 Jump up ^ NBA Official Rules ( 2009 - 2010 ) Rule 10 , Section VII , Penalty . Retrieved July 25 , 2010 Jump up ^ Blinebury , Fran ( June 8 , 2006 ) . `` Rule changes have NBA back in the fast lane '' . Houston Chronicle . Retrieved July 26 , 2010 . Jump up ^ http://www.sportingcharts.com/dictionary/nba/defensive-three-second-violation.aspx Jump up ^ Cruz , Agnes ( January 24 , 2003 ) . `` PBA get fresh look this season '' . Arab News . Retrieved January 13 , 2014 . Jump up ^ `` WNBA Announces Rules Changes for 2013 Season '' . WNBA . Retrieved Dec 16 , 2012 . Basketball ( outline ) General topics History of basketball James Naismith Variations of basketball Leagues Statistics Glossary of terms Index of articles Rules Bonus Jump ball Officials Turnover Violation 3 seconds Offense Defense 5 seconds Basket interference Carrying Double dribble Goaltending Shot clock Traveling Foul Flagrant Personal Technical Game play Air ball Alley - oop Assist Backboard shattering Ball hog Block Buzzer beater Cherry picking Dribble Crossover Dunk Euro step Fadeaway Fast break Fly Flop Jump shot Layup Finger roll Field goal Four - point play Free throw Hook shot Moves Pick and roll Positions Posterized Playbook Rebound Point Screen Back screen Slashing Steal Three - pointer Three - point play Uncontested shot Strategy General Sixth man Offense Continuity offense Flex Shuffle UCLA High Post Wheel Dribble drive motion Four corners Motion Princeton Run and gun Grinnell System Nellie Ball Small ball Triangle Defense 1 - 2 - 1 - 1 1 -- 3 -- 1 2 -- 3 zone Amoeba Box - and - one Double team Full - court press Hack - a-Shaq Jordan Rules Line Man - to - man Match - up zone Triangle - and - two Zone Equipment Backboard Ball Breakaway rim Court Half court Key Net Possession arrow Whistle Clothing Basketball sleeve Finger sleeve Air Jordan Chuck Taylor All - Stars Miscellaneous 100 - point scorers 50 -- 40 -- 90 club AAU All - Americans AAU champions Mikan Drill Player tracking Shootaround Tip drill Winning streaks This basketball - related article is a stub . You can help Wikipedia by expanding it . Retrieved from `` https://en.wikipedia.org/w/index.php?title=Defensive_three-second_violation&oldid=803130800 '' Categories : Basketball penalties Basketball stubs Hidden categories : Wikipedia articles needing clarification from November 2015 All stub articles Talk About Wikipedia Français Edit links This page was last edited on 30 September 2017 , at 17 : 04 . About Wikipedia

Question: when was the defensive 3 second rule implemented