5. Two random variables X and Y are distributed according to the following distribution: se-, zy 20 l0, fx.y(1, v) = zy < 0 a) Find the value of K. b) Show that marginal distributions of X and Y are Gaussian. c) Are X and Y are jointly Gaussian? Please explain. d) Are X and Y independent? Please explain. e) Are X and Y uncorrelated? Please explain. f) Find fx(r |y). Is this a Gaussian distribution? g) Define Z = X +Y. Calculate the mean and variance of Z.

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