3. Suppose X and Y are two random variable with joint pdf f(x,y) = {6(1 - y), 0 ? x ? y ? 1 0, elsewhere (a) Find the marginal density function of X and Y. (b) Compute P(X ? 3/4, Y ? 1/2). (c) Find the conditional pdf of Y given X = x. (d) Compute P(Y ? 3/4|X = 1/2).
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Let the random variables X and Y have joint pdf as follows: f(x, y) = cx + y, 0 < x < 1/2, 0 < y < 1 a. Find the value of constant c. b. Find the marginal densities of X and Y. c. Are the random variables X and Y independent? d. Find the conditional pdf's f1(x|y) and f2(y|x). e. Find E(X) and E(Y). f. Find Var(X) and Var(Y). g. Find Cov(X, Y). h. Find the correlation coefficient of X and Y.
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