Question: Bayesian Estimator Let X1, . .., Xn ~ N(0, 1/7). We assume the prior T ~ Gamma(u, 1/v) whose density is given by f (T

Bayesian Estimator

Let X1, . .., Xn ~ N(0, 1/7). We assume the prior T ~ Gamma(u, 1/v) whose density is given by f (T ) = Tu-le- UT T (u ) Let zu,a be the upper a quantile of Gamma(u,1), i.e., P(7 > Zu,a) = a, y ~ Gamma(u, 1). Note that if T ~ Gamma(u, 1/v), then vr ~ Gamma(u, 1). (1) Find the posterior density f(T|X1, . .., Xn). (2) Find on such that P(T

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