(b) (c) The lifetime, X, of a type of battery is exponentially distributed with mean 500 hours. Let XLXE, X3,X4 and X5 denote the lifetime of ve randomly selected batteries. (i) Use moment generating function method to determine the distribution of the average lifetime, U = W , for the 5 batteries. (6 marks) (ii) State the mean and variance of their average lifetime. (2 marks) Let X1,...,X, be a random sample from a distribution with probability density function f(x)=3xz , 0