Square of Expectation of Product is Less Than or Equal to Product of Expectation of Squares

Theorem
Let $X$ and $Y$ be random variables.

Let the expectation of $X Y$, $\expect {X Y}$, exist and be finite.

Then:


 * $\paren {\expect {X Y} }^2 \le \expect {X^2} \expect {Y^2}$