5. For a randomly selected family with two parents and one male child and one female child: let X1 he the average height of the parents in inches. Let X2 he the height of the {adult} male child and X3 be the height of the {adult} female child. Assume that [X11 X2,X3} follow a multivariate normal distribution with mean and covariance matrix 65 1c2 gm? gm? #2 m and a: m2 102 in}2 an E1n2 in]? 11::2 I {a} 1tall-"hat are the marginal distributions of X2 and X3? 1|vii-"hat are their corre- sponding means? I {h} li-llk'rht- is the correlation between the average parent height and the height of the male child? what is the correlation between the average parent hight and the height of the female child? I {c} 1|L-'qr'hat is the correlation between the heights of the two children? I {d} Conditioned on the mid-parent height X1 2 T5 {tall parents]: what is the joint distribution of [X2,X1}? I {c} From your answer to Ed): what is the mean height of the male child given X1 = T5? 1What is the mean height of the female child given X1 = T5? Compare them with your answer in [d] and provide possible reasons. a {f} From your answer to [d], what is the correlation between the heights of the children once we know X1 = ?5? [This is called conditional correlation]