Question: 5. Let X1, ..., X, be i.i.d. random variables with distribution N(0, o?) and sup- pose the parameter 0 is random with a prior distribution

5. Let X1, ..., X, be i.i.d. random variables with distribution N(0, o?) and sup- pose the parameter 0 is random with a prior distribution N(u, 72). Assume that o', u, 7- are all known. (a) Find the joint probability density function of X = n-1 )"_X; and e. (b) Show that the marginal distribution m(x) of X is N(A, (52) + 72). (c) Derive the posterior distribution (8 X1, . .., X)

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