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(a) Given that X=(X1,X2,,Xn) represents a random sample of size n from a Normal distribution with unknown mean and unknown variance 2 denoted by N(,2) and the prior distribution of is N(0,02), show that the posterior distribution of is N(1,12) where 1=n/2+1/02nX/2+0/02and12=n/2+1/021 (b) Suppose the prior distribution of is N(12,4). A single observation x is taken. Find the posterior distribution for in this case. In the case where 2=6 and x=10, find the posterior probability that >15..

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(a) Given that X=(X1,X2,,Xn) represents a random sample of size n from a Normal distribution with unknown mean and unknown variance 2 denoted by N(,2) and the prior distribution of is N(0,02), show that the posterior distribution of is N(1,12) where 1=n/2+1/02nX/2+0/02and12=n/2+1/021 (b) Suppose the prior distribution of is N(12,4). A single observation x is taken. Find the posterior distribution for in this case. In the case where 2=6 and x=10, find the posterior probability that >15.

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a Given that XX1X2Xn represents a random sample of .pdf

  • 1. (a) Given that X=(X1,X2,,Xn) represents a random sample of size n from a Normal distribution with unknown mean and unknown variance 2 denoted by N(,2) and the prior distribution of is N(0,02), show that the posterior distribution of is N(1,12) where 1=n/2+1/02nX/2+0/02and12=n/2+1/021 (b) Suppose the prior distribution of is N(12,4). A single observation x is taken. Find the posterior distribution for in this case. In the case where 2=6 and x=10, find the posterior probability that >15.