MAS3301 Bayesian Statistics Problems 3 and Solutions

MAS3301 Bayesian StatisticsProblems 3 and SolutionsSemester 22008-9 Problems 31. In a small survey, a random sample of 50 people from a large population is selected. Eachperson is asked a question to which the answer is either Yes or No. Let the proportion inthe population who would answer Yes be .Our prior distribution for is a beta( , )distribution. In the survey, 37 people answer Yes. (a) Find the prior mean and prior standard deviation of .(b) Find the prior probability that < (c) Find the likelihood.(d) Find the posterior distribution of .(e) Find the posterior mean and posterior standard deviation of .(f) Plot a graph showing the prior and posterior probability density functions of on thesame axes.(g) Find the posterior probability that < :The probability density function of a beta(a,b) distribution isf(x) =kxa 1(1 x)b 1wherekis a beta(a,b) then the mean ofXisE(X) =aa+band the variance ofXisvar(X) =ab(a+b+ 1)(a+b) beta(a,b) then you can use a command such as the following in R to find Pr(X < c).

MAS3301 Bayesian Statistics Problems 3 and Solutions Semester 2 2008-9 Problems 3 1. In a small survey, a random sample of 50 people from a large population is selected. Each person is asked a question to which the answer is either \Yes" or \No." Let the proportion in the population who would answer \Yes" be :Our prior distribution for is a ...

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