Maurice Tutor

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Category > Computer Science Posted 27 Jul 2017 My Price 7.00

binomial random variable

Refer to Exercise 16.6. If Y is a binomial random variable based on n trials and success probability p and p has the conjugate beta prior with parameters α = 1 and β = 1,

a determine the Bayes estimator for p, ˆpB.

b what is another name for the beta distribution with α = 1 and β = 1?

c find the mean square for error (MSE) of the Bayes estimator found in part (a).

d For what values of p is the MSE of the Bayes estimator smaller than that of the unbiased estimator ˆp = Y/n?

Exercise 16.6

Suppose that Y is a binomial random variable based on n trials and success probability p (this is the case for the virulent-disease example in Section 16.1). Use the conjugate beta prior with parameters α and β to derive the posterior distribution of p | y. Compare this posterior with that found in Example 16.1.

Example 16.1

Let Y1, Y2, . . . , Yn denote a random sample from a Bernoulli distribution where P(Yi = 1) = p and P(Yi = 0) = 1 − p and assume that the prior distribution for p is beta (α, β). Find the posterior distribution for p.

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Maurice Tutor
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Status NEW Posted 27 Jul 2017 12:07 PM My Price 7.00

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