5.24 Suppose that Y has a multivariate normal distribution with mean, E[Y] = X and V (Y) = 2I, where is a vector of

5.24 Suppose that Y has a multivariate normal distribution with mean, E[Y] = Xθ and V (Y) = σ2I, where θ is a vector of parameters to be estimated, and I is the identity matrix. Write down the likelihood and show that the maximum-likelihood estimate of θ results from minimising with respect to θ the sum-of-squares, S(θ)=(y − Xθ)



(y − Xθ), where y is the observed value of Y. Examine the case when the components of Y are correlated, and when E[Y] = μ(θ).