Statistics | Part IB, 2003

Let X1,,XnX_{1}, \ldots, X_{n} be a random sample from the N(θ,σ2)N\left(\theta, \sigma^{2}\right) distribution, and suppose that the prior distribution for θ\theta is N(μ,τ2)N\left(\mu, \tau^{2}\right), where σ2,μ,τ2\sigma^{2}, \mu, \tau^{2} are known. Determine the posterior distribution for θ\theta, given X1,,XnX_{1}, \ldots, X_{n}, and the best point estimate of θ\theta under both quadratic and absolute error loss.

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