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please help me Problem 9 (20 pt): Random variables X, Y1, Y2 are jointly Gaussian with mean E(X) = 0, E(Y1) = 1, E(Y2) =

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Problem 9 (20 pt): Random variables X, Y1, Y2 are jointly Gaussian with mean E(X) = 0, E(Y1) = 1, E(Y2) = 2 and covariance matrix K = E { X - E( X ) , Y, - E( Y ) , Y, - E(Y2 ) } { X - E(X) , Y1 - E(Y1), Y2 - E(Y2)} = 49 (10) 10 a) Express m(y1, y2) = E (X|Y1 = y1, Y2 = y2) as a function of y1, 92. b) Apply (1) to mapping m(31, y2) to express it as m(y1, y2) ~ a + gly1 + 9292. Provide values of a, 91, 92- c) Now consider the conditional variance of random variable X, g(y1, y2) = E {X -E(X|Yi = y1, Y2 = 2)}' | Vi = y1, Y2 =y2 ] (11) = {r - E(X|Y1 = y1, Y2 = 32)} Px,Ya(xly1, y2)dx Explicitly provide a simple expression of this as a function of y1 and y2

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