Suppose (X1,..., Xk ) has the multivariate normal distribution with unknown mean vector = (1,..., k

Suppose (X1,..., Xk ) has the multivariate normal distribution with unknown mean vector ξ = (ξ1,..., ξk ) and known covariance matrix . Suppose X1 is independent of (X2,..., Xk ). Show that X1 is partially sufficient for ξ1 in the sense of Problem 3.65. Provide an alternative argument for Case 2 of Example 3.9.2.