Random variables X and Y are uniformly distributed over region T enclosed by a triangle displayed by the shade in the right picture. A joint PDF of (X,Y)' up to a unknown constant C is given by f(x, y) = C, for 0 < r < 1, and -I< y < % (1) Determine the value of C. (2) Find the marginal PDF of X. (3) Find the conditional PDF of Y given X = x. (4) Find E(Y|X), and V(Y|X). (5) Find the correlation coefficient Cor(X, Y). Hint: E(Y|X) is a linear function of X. (6) Are X and Y independent or not? Justify your answer.

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