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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Have you seen the Marcinkiewicz_Zygmund Law of Large Numbers?
All you need is a first moment.
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
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