Let $X$ and $y$ again be uniformly distributed independent random variables on $[0,1]$. a) Compute the expected value $E(XY)$. b) What is the probability density function $f_[Z] (z $ of $2=X Y$ ? Hint: First compute the cumulative distribution function $F_{Z}(z)=P(Z \leq z)$ using a double integral, and then differentiate in $2$. c) Use your answer to b) to compute $E(Z)$. Compare it with your answer to a). SP.DL. 2051