Question

A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a disease-free individual's test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than the actual sequence of test results.

 (a) Derive the maximum likelihood estimator of p If n 25 and x = 7, what is the estimate?

 (b) Is the estimator of part (a) unbiased?

 (c) if n=25 and x = 7, what is the mle of the probability (1 - p)⁵ that none of the next five tests done on disease-free individuals are positive? (Round your answer to four decimal places.) 

Answer 1

Sala Cas first point :- The masömum likehold estimator of less sample proportion. Hence, ac = 7, 025 - 2 10:28 L ang (b) option a. las is Xes correct 1 Coj n=25 M LE of x = 7 brobability ClADJO = (1-J 5 241 - 2(1-0.28) 20.193499 ñ 0.1935 Alay