Let the characteristic function of a multivariate normal random vector (X Y Z)' be as follows: P(X Y Z),(s, t, u) = exp{

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Let The Characteristic Function Of A Multivariate Normal Random Vector X Y Z Be As Follows P X Y Z S T U Exp 1 (44.69 KiB) Viewed 68 times

Let the characteristic function of a multivariate normal random vector (X Y Z)' be as follows: P(X Y Z),(s, t, u) = exp{is – iu – s2 – 2t2 – 4u² – 2st + 2su} (a) [5 points] Compute the mean vector and the covariance matrix of the random vector. (b) [5 points] Compute the probability P(x < 2Y). (c) [5 points] Find the conditional distribution of X + Z given that {X + Y = 1} (d) [5 points] Find the conditional distribution of X given that {X = Y, X +Y+ 22 = 0}.