If are pairwise independent and then as

Proof:

Let and . Since are pairwise independent, the are uncorrelated and thus

Since

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# Month: February 2018

# Almost sure convergence via pairwise independence

# An inequality of the mean involving truncation

If are pairwise independent and then as

Proof:

Let and . Since are pairwise independent, the are uncorrelated and thus

Since

Continue reading “Almost sure convergence via pairwise independence”

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Let be i.i.d. r.vs with and . Then

Proof:

First we proove the following useful result

If and then

Note you can find the same lemma on Feller Vol.2 (p. 150) as

Continue reading “An inequality of the mean involving truncation”