EXERCISE 1 Let Y N Nn[:o, E), where Y, o, and Z are partitioned at; follows Q1) (\"l (Eu 2\") ' Y = , = , E = , and let A be a matrix such that AZ 2 E . ( Q2 H #2 E21 E22 22 12 a. Let U = Q1 AQ2 and V = Q2. Find the joint distribution of U and V. b. Show that Q1|Q2 N N011 + A(Q2 [412}, 211 1122311,). EXERCISE 2 Suppose the following random wrriables for adult men Variable Description Y1 Percent body fat from Siri's (1956) equation Y2 Age (years) Y3 Weight (lbs) Y4 Height (inches) Y5 Abdomen circumference (cm) follow multivariate normal with mean vector and variance covariance matrix as follows: Mean vector: 19 45 179 70 93 Variance-covariance matrix: y1 y2 y3 y4 y5 y1 70 31 151 '-3 74 y2 31 154 -2 -3 31 y3 151 -2 866 33 283 y4 -3 -8 33 13 3 y5 ?4 31 283 3 117 Find the conditional distribution of the percent body fat Y1 given Y2, K3, Y4