Chapter 6.2, Problem 24E

A vehicle with a particular defect in its emission control system is taken to a succession of randomly selected mechanics until r = 3 of them have correctly diagnosed the problem. Suppose that this requires diagnoses by 20 different mechanics (so there were 17 incorrect diagnoses). Let p = P(correct diagnosis), so p is the proportion of all mechanics who would correctly diagnose the problem. What is the mle of p? Is it the same as the mle if a random sample of 20 mechanics results in 3 correct diagnoses? Explain. How does the mle compare to the estimate resulting from the use of the unbiased estimator given in Exercise 17?