Probability

Concept:For independent random variables, the expectation of their product equals the product of their expectations.Explanation:• Option A: $E(x y)=E(x)\times E(y)$ is a fundamental property of independent random variables.• Option B: $E(x y)=E(x)+E(y)$ is incorrect; expectation of product is not generally the sum.• Option C: $E(x+y)=E(x)+E(y)$ always holds by linearity of expectation, regardless of independence.• Option D: $E(x-y)=E(x)-x E(y)$ is not a valid expression (contains an $x$ inside the expectation incorrectly).The property uniquely true when $x$ and $y$ are independent is Option A.Answer:A. $E(x y)=E(x)\times E(y)$