Let be iid random variables with mean and . Set . Show almost surely as .

So far all I have is convergence in probability from the weak law of large numbers. I don't see what the trick is to using the expected value.

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- Dec 13th 2011, 05:53 PMBeakyalmost sure convergence
Let be iid random variables with mean and . Set . Show almost surely as .

So far all I have is convergence in probability from the weak law of large numbers. I don't see what the trick is to using the expected value. - Dec 13th 2011, 07:33 PMmatheagleRe: almost sure convergence
Have you seen the Marcinkiewicz_Zygmund Law of Large Numbers?

All you need is a first moment. - Dec 13th 2011, 10:50 PMMooRe: almost sure convergence
But maybe his exercise is to prove it with the 4th moment !!

Which is a common proof, but the margin is too narrow to put it down. At least right now :D