申論題

3.Suppose that X is a father's height, Y is a mother's height, Z is a child's ultimate height (as an adult), and G is delined as: G = I if the child is a boy and G = -I ifthe child is a girl. Let M = (X+ Y)/2. Suppose that, conditional on known values of G, X, and Y, Z has a continuous uniform distribution with range [M -5 +3G, M + 5 + 3G]. If a girl's father is 4 inches taller than her mother, the probability that she will grow to be taller than her mother is__________.