15. Let X be a continuous random variable with density function f . A number t is said to be the median of X if P (X ≤ t) = P (X ≥ t) = 1 2 .

By Exercise 7, Section 6.1, X is symmetric about α if and only if for all x we have f (α − x) = f (α + x). Show that if X is symmetric about α, then E(X) = Median(X) = α.