Random variables and probability distributions Law of Large
Numbers Introduction to the law of large numbers Law of Large
Numbers ⇐ Use this menu to view and help create subtitles for
this video in many different languages. You'll probably want to
hide YouTube's captions if using these subtitles. - Let's learn
a little bit about the law of large numbers - which is on many
levels, one of the most intuitive laws - in mathematics and in
probability theory. - But because it's so applicable to so many
things, it's often - a misused law or sometimes, slightly
misunderstood. - So just to be a little bit formal in our
mathematics, - let me just define it for you first and - then
we'll talk a little bit about the intuition. - So let's say I
have a random variable, X. - And we know its expected value or
its population mean. - The law of large numbers just says that -
if we take a sample of n observations of our random variable, -
and if we were to average all of those observations-- - and let
me define another variable