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5 Let Y1Y2Yn be independent and identically distributed.pdf

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5. Let Y1,Y2,,Yn be independent and identically distributed Negative Binomial(1,) random variables. Suppose that the prior distribution of follows the Beta(,). (i) Find the posterior distribution of ,(X). (ii) Given the prior distribution of is Beta(=3,=12) and i=124xi=13.00, obtain a 99% highest posterior density credible region for C>0. (iii) Use the results of (i) and (ii) to determine the posterior odds ratio for testing the hypotheses H0:0.85 vs H1:>0.85..

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5. Let Y1,Y2,,Yn be independent and identically distributed Negative Binomial(1,) random variables. Suppose that the prior distribution of follows the Beta(,). (i) Find the posterior distribution of ,(X). (ii) Given the prior distribution of is Beta(=3,=12) and i=124xi=13.00, obtain a 99% highest posterior density credible region for C>0. (iii) Use the results of (i) and (ii) to determine the posterior odds ratio for testing the hypotheses H0:0.85 vs H1:>0.85.

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