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= If n = 20 and x = 5, what is the estimate? p = (b) Is the estimator of part (a) unbiased? O Yes O No (c) If n = 20 and x = 5, 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.)
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= If n = 20 and x = 5, what is the estimate? p = (b) Is the estimator of part (a) unbiased? O Yes O No (c) If n = 20 and x = 5, 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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 =
If n = 20 and x = 5, what is the estimate?
p=
(b) Is the estimator of part (a) unbiased?
Yes
No
(c) If n = 20 and x = 5, 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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1665bdf4-5411-4ca1-a903-736ef5c9444c%2F6cf7caa3-c84c-40ff-8a18-f1d026d809fd%2F9hk9ti_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 =
If n = 20 and x = 5, what is the estimate?
p=
(b) Is the estimator of part (a) unbiased?
Yes
No
(c) If n = 20 and x = 5, 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.)
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