5. 15 pt The time (in hours) required to repair a machine is an exponentially distributed random variable with parameter /\\ : %. Compute each of the following: (a) 2 pt The mean and the variance of the repair time of a machine. (b) 2 pt The probability that a repair time exceeds 2 hours. (c) 3 pt The conditional probability that a repair takes at least 10 hours, given that its duration exceeds 9 hours. Now, suppose that there are two machines that need to be repaired: the machine 1 is repaired rst, and then the machine 2 is repaired. Suppose that the repair time of the two machines are independent from each other, and the repair time of each machine is an exponentially distributed random variable with parameter A = ;. Compute each of the following: (d) 3 pt The PDF, the mean, and the variance of the total repair time. (e) 2 pt The probability that the total repair time exceeds 4 hours. (f) 3 pt The PDF, the mean, and the variance of the difference between the repair time of the machine 1 and the repair time of the machine 2