Question

Let X and Y be two independent random variables. Which one of the relations between expectation (E), variance (Var) and covariance (Cov) given below is FALSE?

• A. E(XY) = E(X) E(Y)
• B. Cov (X, Y) = 0
• C. Var (X + Y) = Var (X) + Var (Y)
• D. $E\left(X^2{Y}^2\right)=\left(E\right(X\left){)}^2\right(E\left(Y\right){)}^2$

Answer 1

The correct option is D $E\left(X^2{Y}^2\right)=\left(E\right(X\left){)}^2\right(E\left(Y\right){)}^2$

$E\left(X^2{Y}^2\right)=\left[E\right(X\left){]}^2\right[E\left(Y\right){]}^2$

All other option are true for two independent random variables.