Question

If $X$ and $Y$ are independent non-degenerated random variables then $Var(XY)=Var(X)\cdot Var(Y)$ iff

• A. $E(X)\ne0$ and $E(Y)\ne0$
• B. $E(X)=0$ and $E(Y)\ne0$
• C. $E(X)\ne0$ and $E(Y)=0$
• D. $E(X)=0$ and $E(Y)=0$

Hint:

Memory aid: The variance of a product is the product of the variances ONLY when both variables are centered at zero (mean = 0). If the means are non-zero, the variance of the product is always larger than the product of the variances.

Answer 1

The Correct Option is D