31. At time t  0, 20 identical components are put on test. The lifetime distribution of each is exponential with parameter l. The experimenter then leaves the test facility unmonitored. On his return 24 hours later, the experimenter immediately terminates the test after noticing that y  15 of the 20 components are still in operation (so 5 have failed). Derive the mle of l. [Hint: Let Y  the number that survive 24 hours. Then Y  Bin(n, p). What is the mle of p?

Now notice that p  P(Xi  24), where Xi is exponentially distributed. This relates l to p, so the former can be estimated once the latter has been.]