Question-51

Variance

Let \(X\) and \(Y\) be independent random variables with \(E[X] = 3, E[Y] = 2, \text{Var}(X) = 1\) and \(\text{Var(Y)} = 4\). Find the variance of the product \(Z = XY\).

Hint

Use the concept of “Independence of two random variables”, i.e., if \(X\) and \(Y\) are two independent random variables then \(E[XY] = E[X]E[Y]\)

Answer

Solution