Let X be an exponentially distributed random variable with probability density function (PDF) given by fx (x) = le-Ax x 20 otherwise Consider the random variable Y = VX. (a) Give an algorithm for generating the random variable Y from a standard uniform random variable U. (b) What is the mean and mode of the random variable Y? (c) Choose a value for the parameter 1 so that the mean of the random variable Y is 5, i.e., E(Y) = 5