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Let X and Y be independent binomial random variables with parameters (m, 0.8) and (200 m, 0.2), respectively, where m is unknown and m {0, 1, 2,., 200}. Let Z = X+Y. (a) Find the maximum likelihood estimate of m based on Z. (b) What are the expected value and standard deviation of the above estimate? (c) Construct an approximate 95% confidence interval for m, assuming the observed value of Z is 124.

Let X and Y be independent binomial random variables with parameters (m, 0.8) and (200 m, 0.2), respectively, where m is unknown and m {0, 1, 2,., 200}. Let Z = X+Y. (a) Find the maximum likelihood estimate of m based on Z. (b) What are the expected value and standard deviation of the above estimate? (c) Construct an approximate 95% confidence interval for m, assuming the observed value of Z is 124.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 8CR
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Let X and Y be independent binomial random variables with parameters (m, 0.8) and (200 – m, 0.2), respectively, where m is unknown and m e {0, 1, 2, ... , 200}. Let Z = X + Y. (a) Find the maximum likelihood estimate of m based on Z. (b) What are the expected value and standard deviation of the above estimate? (c) Construct an approximate 95% confidence interval for m, assuming the observed value of Z is 124.
Transcribed Image Text:Let X and Y be independent binomial random variables with parameters (m, 0.8) and (200 – m, 0.2), respectively, where m is unknown and m e {0, 1, 2, ... , 200}. Let Z = X + Y. (a) Find the maximum likelihood estimate of m based on Z. (b) What are the expected value and standard deviation of the above estimate? (c) Construct an approximate 95% confidence interval for m, assuming the observed value of Z is 124.
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