A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X - the number among then 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. p- 0.12 If n= 25 and x- 3, what is the estimate? p- 0.12 (b) Is the estimator of part (a) unbiased? O Yes O No (c) If n- 25 and x- 3, 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.) 0.5277
A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X - the number among then 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. p- 0.12 If n= 25 and x- 3, what is the estimate? p- 0.12 (b) Is the estimator of part (a) unbiased? O Yes O No (c) If n- 25 and x- 3, 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.) 0.5277
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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![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.
p = 0.12
If n = 25 and x = 3, what is the estimate?
0.12
(b) Is the estimator of part (a) unbiased?
O Yes
O No
(c) If n = 25 and x = 3, 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.)
0.5277](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86bfc21f-7304-4d6a-8ae3-de059a5180e7%2F6531cbb4-ba5b-4a5a-96e9-ee10fc2e27a4%2Fkylo0x_processed.png&w=3840&q=75)
Transcribed Image Text: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.
p = 0.12
If n = 25 and x = 3, what is the estimate?
0.12
(b) Is the estimator of part (a) unbiased?
O Yes
O No
(c) If n = 25 and x = 3, 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.)
0.5277
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