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I'm confused about the conditional distribution. Thank you 2. Let X = (X, Y) be multivariate Gaussian with # = EX = (9) . E

I'm confused about the conditional distribution. Thank you

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2. Let X = (X, Y) be multivariate Gaussian with # = EX = (9) . E = Var(X ) = (1/2 1 1/2 1 (i) (4 pts) Determine the conditional distribution of X given Y. (ii) (3 pts) Determine the conditional distribution of 2X + 1 given Y. (iii) (3 pts) Compute S = El/2. (iv) (3 pts) Find the distribution of Z = S-(X - /). (v) (2 pts) Find the distribution of || Z |2. (vi) (4 pts) Find a linear combination a X +a,Y = a X that maximizes Var(a X)/la| |2. What is the maximum

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