A plant supervisor is interested in budgeting weekly repair costs for a certain type of machine. Records over the past years indicate that these repair costs have an exponential distribution with mean 20 for each machine studied. Let Y1, Y2, . . . , Y5 denote the repair costs for five of these machines for the next week. Find a number c such that assuming that the machines operate independently. [Hint: Use the result given in Exercise 7.93.]
If Y has an exponential distribution with mean θ, show that U = 2Y/θ has a χ 2 distribution with 2 df.