Suppose the random variables X, Y, and Z have the joint probability density function f(x, y, z) = 8xyz for 0 < x < 1, 0 < y < 1, and 0 < z < 1. Determine the following:
(a) P(X < 0.5)
(b) P(X < 0.5, Y < 0.5)
(c) P(Z < 2)
(d) P(X < 0.5, Z < 2)
(e) E(X)