Let X 1 ,...,X n be i.i.d. random variables having the normal density with mean 0 and variance    Also, let π(θ) have the gamma density with scale parameter σ 2 and shape parameter ν. Obtain the...

Let X₁,...,X_n
be i.i.d. random variables having the normal density with mean 0 and variance

 Also, let π(θ) have the gamma density with scale parameter σ²
and shape parameter ν. Obtain the posterior density of θ, and examine its mean and median. Are these the same? Examine any stochastic ordering of the two Bayes estimators under the squared error and absolute error loss.