Ex. 3.7 Assume y; ~ N(Bo + x3,0),i=1,2,..., N, and the parameters B, j = 1,...,p...

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Ex. 3.7 Assume y; ~ N(Bo + x3,0²),i=1,2,..., N, and the parameters B₁, j = 1,...,p are each distributed as N(0, 72), independently of one another. Assuming o2 and 72 are known, and Bo is not governed by a prior (or has a flat improper prior), show that the (minus) log-posterior density of 3 is proportional to ₁1(i3o - EjBj)² + ₁ =18² where X = 02/7². Ex. 3.7 Assume y; ~ N(Bo + x3,0²),i=1,2,..., N, and the parameters B₁, j = 1,...,p are each distributed as N(0, 72), independently of one another. Assuming o2 and 72 are known, and Bo is not governed by a prior (or has a flat improper prior), show that the (minus) log-posterior density of 3 is proportional to ₁1(i3o - EjBj)² + ₁ =18² where X = 02/7².

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