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а- Find the maximum likelihood estimator (MLE) of p. b- Is the family of Beta distributions [Beta (a;ß): a > 0; B>0] a conjugate family for samples from the Geometric distributions [Geo(p): 00 are known constants. C- Derive the Bayes estimator of p. d- Express the estimator in part (c) as a weighted average of the prior mean of p and the MLE of p.

а- Find the maximum likelihood estimator (MLE) of p. b- Is the family of Beta distributions [Beta (a;ß): a > 0; B>0] a conjugate family for samples from the Geometric distributions [Geo(p): 00 are known constants. C- Derive the Bayes estimator of p. d- Express the estimator in part (c) as a weighted average of the prior mean of p and the MLE of p.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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iid X1,..., Xn Geo(p) where 0 <p<1 is unknown. а- Find the maximum likelihood estimator (MLE) of p. b- Is the family of Beta distributions [Beta (a;B): a >0; B>0]a conjugate family for samples from the Geometric distributions [Geo(p): 0 <p< 1]? Suppose the prior distribution of p is Beta (a;B) where a;ß >0 are known constants. C- Derive the Bayes estimator of p. d- Express the estimator in part (c) as a weighted average of the prior mean of p and the MLE of p.
Transcribed Image Text:iid X1,..., Xn Geo(p) where 0 <p<1 is unknown. а- Find the maximum likelihood estimator (MLE) of p. b- Is the family of Beta distributions [Beta (a;B): a >0; B>0]a conjugate family for samples from the Geometric distributions [Geo(p): 0 <p< 1]? Suppose the prior distribution of p is Beta (a;B) where a;ß >0 are known constants. C- Derive the Bayes estimator of p. d- Express the estimator in part (c) as a weighted average of the prior mean of p and the MLE of p.
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