3.2 Let X : 5 × 1 denote the vector of demand for 5 separate items in a retail business, and L(X|θ, ) = N(θ, ). Suppose that for fixed, θ follows the natural conjugate prior distribution L(θ| ) = N(2e, ), where e’ = (1,1,1,1,1), and suppose follows the natural conjugate prior distribution L( ) = W–1(H,5,10), where Suppose that independent observations of X taken at 11 random times yield the summary statistics for the sample mean vector and unnormed sample covariance matrix Find the joint posterior density for θ and given the sample data, and express the density in its simplest numerical form, wherever possible. (Combine all matrix products, invert any matrices, evaluate any determinants, and so on.)