A supplier of kerosene has a weekly demand Y possessing a probability density function given by y, 0 y 1, f(y) 1, 1y1.5, 0, elsewhere, with measurements in hundreds of gallons. (This problem was introduced in Exercise 4.13.) The supplier's profit is given by U = 10Y - 4. a Find the probability density function for U. b Use the answer to part (a) to find E(U). c Find E(U) by the methods of Chapter 4.