Homework Help is Here – Start Your Trial Now!
Math
Probability
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

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
See similar textbooks
icon
Related questions
Question

I need help with this question as I am stuck

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
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
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
SEE MORE TEXTBOOKS