Let X, Y be two random variables such that the conditional density function of Y given that Xx is e-y/2, 0≤y<∞, elsewhere. f(y\X = x) = { { {e-u/², 0, Suppose that P(X = 4) = 1. (a) Find the unconditional mean and variance of Y Now suppose that X is a Geometric random variable with p = 1/4. (b) Find the conditional mean and variance of Y given X = x. (c) Find the unconditional mean and variance of Y and compare to the mean and variance in (a).

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A: (b)

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A: a) The required value is calculated as follows: fx=ddxFx      =ddxx24     =2x4     =x2…

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