Problem 5 Let Y = (Y Y2 ... Yn.) T be a random vector taking on values in R" with mean / E Rn and covariance matrix E. Also let 1 be the ones vector defined by 1 = (1 1 ... 1) 5.i Find the projection matrix Hy where V is the subspace generated by 1. 5.ii Show that Hy is symmetric and idempotent. 5.iii Let x = (a a .. a) , where a E R". Show that Hyx = X. 5.iv Find the projection of Y onto the subspace generated by 1. That is, compute Hy Y. 5.v Compute the mean and variance of Hy Y