text: Integration of a pdf, expected value
  
  • alias
  
  Homework Statement
  
  Show that E[Y^4] = 3, where Y~N(0,1)
  
  Homework Equations
  
  E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3
  E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2)
  
  The Attempt at a Solution
  
  I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's possible to solve the second using integration by parts but I can't find what to use for
  [u, du, dv, v] in order to integrate by parts. Any help would be appreciated. Thanks.
  
  Sorry, it's a definite integral in from -inf to inf.
  
  Homework Statement
  
  Show that E[Y^4] = 3, where Y~N(0,1)
  
  Homework Equations
  
  E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3
  E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2)
  
  The Attempt at a Solution
  
  I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's possible to solve the second using integration by parts but I can't find what to use for
  [u, du, dv, v] in order to integrate by parts. Any help would be appreciated. Thanks.
  
  You might have to try several things until you get something that will work. What have you tried so far? Another approach that is often useful is to look at dI(a)/da or d^2I(a)/da^2, where I(a) = integral_{y=-inf..inf} exp(-a*y^2/2) dy.
  
  RGV
  
  I tried integration by parts but the integral I end up with makes no sense to me.
  
  I tried integration by parts but the integral I end up with makes no sense to me.
  
  If you show your work we have the basis of a discussion.
  
  RGV
  
  Just spit-balling, is there a way to use some substitutions to make this look something like the pdf of a gamma distribution? Then use what you know about that?
  
  I integrated the Gaussian distribution, it took a long time but I finally got the right answer. After making a substitution, integration by parts worked. I would like to know if the formula: E[(Y-mu)^4]/[E(Y-mu)^2]^2, is useless for answering this question though. Thanks guys.
explanation: The document is a discussion thread from a homework help forum. It contains a math question about showing that the expected value \( E[Y^4] = 3 \) for a standard normal random variable \( Y \). The thread includes the user's attempt at solving the problem, a suggestion from another user to try integration by parts and other methods, and the user's response indicating they eventually solved the problem using a substitution and integration by parts. The document also includes a follow-up question about the usefulness of a specific formula.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Integration of a pdf, expected value
  
  • alias
  
  Homework Statement
  
  Show that E[Y^4] = 3, where Y~N(0,1)
  
  Homework Equations
  
  E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3
  E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2)
  
  The Attempt at a Solution
  
  I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's possible to solve the second using integration by parts but I can't find what to use for
  [u, du, dv, v] in order to integrate by parts. Any help would be appreciated. Thanks.
  
  Sorry, it's a definite integral in from -inf to inf.
  
  Homework Statement
  
  Show that E[Y^4] = 3, where Y~N(0,1)
  
  Homework Equations
  
  E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3
  E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2)
  
  The Attempt at a Solution
  
  I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's possible to solve the second using integration by parts but I can't find what to use for
  [u, du, dv, v] in order to integrate by parts. Any help would be appreciated. Thanks.
  
  You might have to try several things until you get something that will work. What have you tried so far? Another approach that is often useful is to look at dI(a)/da or d^2I(a)/da^2, where I(a) = integral_{y=-inf..inf} exp(-a*y^2/2) dy.
  
  RGV
  
  I tried integration by parts but the integral I end up with makes no sense to me.
  
  I tried integration by parts but the integral I end up with makes no sense to me.
  
  If you show your work we have the basis of a discussion.
  
  RGV
  
  Just spit-balling, is there a way to use some substitutions to make this look something like the pdf of a gamma distribution? Then use what you know about that?
  
  I integrated the Gaussian distribution, it took a long time but I finally got the right answer. After making a substitution, integration by parts worked. I would like to know if the formula: E[(Y-mu)^4]/[E(Y-mu)^2]^2, is useless for answering this question though. Thanks guys.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a discussion thread from a homework help forum. It contains a math question about showing that the expected value \( E[Y^4] = 3 \) for a standard normal random variable \( Y \). The thread includes the user's attempt at solving the problem, a suggestion from another user to try integration by parts and other methods, and the user's response indicating they eventually solved the problem using a substitution and integration by parts. The document also includes a follow-up question about the usefulness of a specific formula.
  
  Label: question-and-answer