A rod of length L is bent until it snaps in two. The point of breakage X, as measured from one end of the rod, has a probability density function
f(x) = Ax(L - x)
for 0 < x < L.
(a) What is the value of A?
(b) What is the probability density function of the difference in the lengths of the two pieces of the rod?
(c) What is the expected difference in the lengths of the two pieces of the rod?