In: Statistics and Probability
Let X and Y be uniformly distributed independent random variables on [0, 1].
a) Compute the expected value E(XY ).
b) What is the probability density function fZ(z) of Z = XY
?
Hint: First compute the cumulative distribution function FZ(z) =
P(Z ≤ z) using a double integral, and then differentiate in z.
c) Use your answer to b) to compute E(Z). Compare it with your answer to a).