Question

Suppose that \(X\) and \(Y\) are independent random variables with probability densities \[ f_X(x)= \begin{cases} \dfrac{8}{x^3}, & x>2,[2mm] 0, & \text{elsewhere}, \end{cases} \qquad f_Y(y)= \begin{cases} 2y, & 0 0, & \text{elsewhere}. \end{cases} \] Then the expected value of \(Z=XY\) is

• A. \(\dfrac{4}{3}\)
• B. \(\dfrac{8}{3}\)
• C. \(\dfrac{1}{3}\)
• D. \(1\)

Hint:

If \(X\) and \(Y\) are independent, \[ \boxed{ E(XY)=E(X)\,E(Y). } \]

Answer 1

The Correct Option is B