# Infinite product of indpt. random variables

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• May 7th 2012, 12:21 AM
sweetadam
Infinite product of indpt. random variables
Hi everyone,

Just a quick Q:

In one of my question I see a statement that:

Let $Z_1$, $Z_2$... be indpt. non-negative random variables have mean 1.

$E[\prod_{i=1}^{\infty} {Z_i} ] \leq \prod_{i=1}^{\infty} E[Z_i]\leq1$

Does anyone know what is this inequality called? so that I can find a proof for it

Thanks.