Let X,..., Xn be i.i.d. N(u, o2) variables where and o2 are both unknown. Consider the...

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Let X₁,..., Xn be i.i.d. N(u, o2) variables where and o2 are both unknown. Consider the prior (μ, o²) x 1/0². Show that the posterior predictive distribution of a future observation Xn+1 is a t distribution with n-1 d.f., location X and scale (1+1/n)¹/2s where s² = = n²₁ Ei=1(Xi-Xn)². n-1 Let X₁,..., Xn be i.i.d. N(u, o2) variables where and o2 are both unknown. Consider the prior (μ, o²) x 1/0². Show that the posterior predictive distribution of a future observation Xn+1 is a t distribution with n-1 d.f., location X and scale (1+1/n)¹/2s where s² = = n²₁ Ei=1(Xi-Xn)². n-1

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