Problem 4. Suppose that in a certain large population mothers' heights X and daughters' heights Y are both normally distributed with mean 65 inches and standard deviation 3 inches. Suppose further that mothers' and daughters' heights are jointly normal (ie., they are bivariate normal variables) with correlation 1/2. (a) Among all daughters whose mothers were approximately 68 inches tall, what fraction are taller than their mothers? (b) What fraction of all mother/ daughter pairs have average height above 66 inches? (c) What is the average height of all mothers with above-average heights, that is, what is E(X | X > 65)