Suppose that X1, , Xn are i i d having the normal distribution with mean and precision given (, ) Let (, ) have the usual improper prior Let '2 s2n (n 1) Prove that the posterior distribution of V (n 1) '2 is the 2 distribution with n 1 degrees of freedom

Question: Suppose that X1, . . . , Xn are i.i.d. having the normal distribution with mean and precision given (, ). Let

Suppose that X1, . . . , Xn are i.i.d. having the normal with mean μ and precision τ given (μ, τ ). Let (μ, τ ) have the usual improper prior. Let σ'2 = s2n/(n − 1). Prove that the posterior of V = (n − 1)σ'2τ is the χ2 with n − 1 degrees of freedom.

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