X1 8. The random vector Y = - - - where X1 = and X2 = has a Ns(p, E) where a' = (0, 0, 0, 0,0) and 4.2 -0.01 -0.08 -0.32 -0.89 -0.01 3.56 -0.25 0.3 -1.28 E= -0.08 -0.25 2.16 0.55 0.07 -0.32 0.3 0.55 2.63 0.74 -0.89 -1.28 0.07 0.74 2.45 Let pra and Eye be the mean and the covariance matrix of the conditional distribu- tion of X1 given X; = (1, 1,0). (a) (7 points) Calculate #12. (Use R. for this. You must provide the R code and all outputs) (b) (8 points) Calculate |Zip). [Exel and and their product (E12) x |Exel. Now cal- culate |2 and comment on your results. Important Definition: A p-dimensional random vector X is said to have a multivariate Normal distribution with mean vector , and covariance matrix Z if its p.d.f. is given by f(x) = (21)-P/2|E-1/2expl-= (x - M)'E-1(x - M)],x ERP We write X ~ Np (u, E)