Let X have a uniform distribution on the interval (0, 2). Given X = x, let Y have a (conditional) uniform distribution on the interval (0,0.5x). (a) Write down the conditional pdf of Y given that X = x. Be sure to include the support of Y. (b) Find E(Y|x) and E(Y). (c) Determine f(x, y), the joint pdf of X and Y. (d) Find fy(y), the marginal pdf of Y. (e) Find g(xly), the conditional pdf of X given Y = y.

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