let x x1 x2 x3 be a 3 dimensional gaussian random vector with expected value vector and covariance matrix 2 cx 2 2 2 ex compute the correlation matrix of x that is rx b find the marginal pro 80933
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X and Y are random variables with a correlation coefficient of 0.75, and with E[X] = Var[X] = 1, and E[Y] = Var[Y] = 2. Find Var[X 2Y].
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2. For any two random variables X and Y with finite variances, prove that(a) Cov(X, Y) = Cov(X, E[Y|X]).(b) X and Y - E[Y|X] are uncorrelated.(c) Var(Y - E[Y|X]) = E[Var(Y|X)].
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