Question

A vehicle with a particular defect in its emission control system is taken to a succession of randomly selected mechanics until r = 17 of them have correctly diagnosed the problem. Suppose that this requires diagnoses by 200 different mechanics (so there were 3 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 17 correct diagnoses? Explain No, the formula for the first one is (number of failures)/(number of trials) and the formula for the second one is (number of successes)/(number of failures) No, the formula for the first one is (number of successes)/(number of failures) and the formula for the second one is (number of failures)/(number of trials) Yes, both mles are equal to the fraction (number of successes)/(number of trials) Yes, both mles are equal to the fraction (number of successes)/(number of failures) No, the formula for the first one is (number of failures)/(number of trials) and the formula for the second one is (number of successes)/(number of trials) r-1 How does the mle compare to the estimate resulting from the use of the unbiased estimator p rx1 OThe mle is greater than the the unbiased estimator The mle is equal to the the unbiased estimator The mle is less than the the unbiased estimator

Answer 1

Coolertion:- x- incorrect answer (diagonses) random variable, ne has a -ve binomial with parametar o a he likelihood buck'on f (x); P, e) - (***) p(laps? | 7 n 4 - 11 Inf[(x; p)] = ln trenptalncirp) devation on both sides. Apply zenle (x; p)] = 2 2 - 4 - *- (+Wp Pliope - -(040) P ~ Ñ - PC1-p T Y +24,

 - mtu as no or incorrect diagonsis. 53 = 17 (comect diagonsis ro 85 =0.85 17+3 P : 1 : Tê= 0.85 bles Yes, both are equal to the fraction number of success - no. of trials option 'c'l is right Answes. b) unbiased estimator i ry rtu-1 17-1 0944+*, 5 173-7 unbiaseel esimator = 0.842 The me is greater than unbiased estimator, ..