Censored Data. A common problem in indus try is life testing of components and systems. In this problem, we will assume that lifetime has an exponen- tial distribution with parameter A, so j = 1/4 = T is an unbiased estimate of p. When a components are tested until failure and the data X. X. X, represent actual lifetimes, we have a complete sample, and is indeed an unbiased estimator of p. However, in many situations, the components are only left under test until a failures have occurred. Let Y, be the time of the first failure, Y be the time of the second failure...., and Y, be the time of the last failure. This type of test results in censored data. There are n-units still running when the test is terminated. The total accumulated test time at termination is 1 = x+(-1)x

(a) Show that =T/r is an unbiased estimator for [Hint: You will need to use the memoryless property of the exponential distribution and the results of Exercise