 Expectation of a product of independent random variables (source code)

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= Expectation of a product of independent random variables
{title2=$\mathbb E\prod_iX_i=\prod_i\mathbb E X_i$}

For independent integrable variables, $\mathbb E\prod_iX_i=\prod_i\mathbb E X_i$. <Tonelli theorem> first gives $\mathbb E\prod_i|X_i|=\prod_i\mathbb E|X_i|<\infty$; then <Fubini's theorem> factors the signed joint integral.

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