Question: solve this problem Consider the Bayesian linear model y, ~ N(xi8, 07), i=1,...,n, where Soa, = 0, Soe? =n and Sow, =7 i=1 i=1 i=1

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Consider the Bayesian linear model y, ~ N(xi8, 07), i=1,...,n, where Soa, = 0, Soe? =n and Sow, =7 i=1 i=1 i=1 The prior for @ is given by (8) = 0.5 1(8 = 0) + 0.5 N(6|0,7), where 1(( = 0) is the probability mass function which puts all probability on 6 = 0. Suppose o and 7 are known. (1) (8 pts) Write down the posterior density for 8 and note that this is always of the form prior times likelihood

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