Consider two random variables X and Y with following probability distribution functions: F(x, y) = KX²y² 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 a) Find value of K such that this be a valid distribution function. b) Find marginal distribution function of Y. c) Find conditional distribution function of F(x| Y ≤ 0.5).

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