30. At time t
0, 20 identical components are put on test. The lifetime distribution of each is exponential with parameter .

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 . [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  to p, so the former can be estimated once the latter has been.]