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Let X1,...,Xn∼iid Gamma(3,1/θ) and we assume the prior for θ is InvGamma(10,2). (a) Find the posterior...

Let X1,...,Xn∼iid Gamma(3,1/θ) and we assume the prior for θ is InvGamma(10,2). (a) Find the posterior distribution for θ. (b) If n= 10 and   ̄x= 18.2, find the Bayes estimate under squared error loss. (c) The variance of the data distribution is φ= 3θ2. Find the Bayes estimator (under squared error loss) for φ.Let X1,...,Xn∼iid Gamma(3,1/θ) and we assume the prior for θ is InvGamma(10,2). (a) Find the posterior distribution for θ. (b) If n= 10 and   ̄x= 18.2, find the Bayes estimate under squared error loss. (c) The variance of the data distribution is φ= 3θ2. Find the Bayes estimator (under squared error loss) for φ.

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