1. Suppose that we have N observations denoted by x = (x1,..., N), from an autoregressive (AR) model of order 1. Therefore data is generated by the process, xt = axt-1 + Et, t = 2,..., N, where Et~ (iid) N (0,7-¹). Suppose that we specify a prior distributions for a: a ~ N(0, 0a), and a gamma prior for T: T~ Gamma (a, B). (a) Calculate the full posterior conditional distribution of 7. (b) Calculate the full posterior conditional distributions of a.

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