Question: Y is a discrete random variable with P {Y = 1} = P {Y = 1} = 0.4, P {Y = 2} = 0.2.

Y is a discrete random variable with P {Y = 1} =

Y is a discrete random variable with P {Y = 1} = P {Y = 1} = 0.4, P {Y = 2} = 0.2. When Y is known, X is Gaussian with E[X] = Y and Var (X) = Y. (a) Find E [X]. (b) Find E [X]. (c) Find Var (X). (d) Find E[XY]. (e) Find the correlation coefficient between X and Y. (f) Are X and Y independent? Explain why. (g) Find the pdf of X.

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