Expectation of Product of Independent Random Variables is Product of Expectations/Corollary

Corollary to Expectation of Product of Independent Random Variables is Product of Expectations
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space. Let $X$ and $Y$ be integrable random variables that are independent.

Then:


 * $\expect {X Y} = \expect X \expect Y$

Proof
We have: