Repeat the previous question with a uniform prior for . Data From previous Question We will use

Repeat the previous question with a uniform prior for .

Data From previous Question

     

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We will use the Minitab macro BinoGCP or the R function binogcp to nd the posterior distribution of the binomial probability when the observation distribution of Y is binomial(n) and we have a general continuous prior for Suppose the prior has the shape given by . for 2 2 for 2 < 3 9( ) = 5 for 3 < 5 0 for 5 < Store the values of and prior g( ) in columns c1 and c2, respectively. Suppose out of n = 20 independent trials, y = 7 successes were observed. (a) [Minitab:] Use Bino GCP to determine the posterior distribution g(y). Details for invoking Bino GCP are given in Appendix C. [R:] Use binogcp to determine the posterior distribution g(y). De- tails for using binogcp are given in Appendix D. (b) Find a 95% credible interval for by using tintegral in Minitab, or the quantile function in R. upon the results of binogcp.