5. Let X have a uniform distribution on the interval (0,2). Given X = x, let Y have a (conditional) uniform distribution

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5. 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, 2x). (a) Write down the conditional probability density function of Y given that X = x. Make sure to include the support of Y for each possible value of x. (b) Find E(Y|C) and E(Y).

(c) Find Var(Y|C) and Var(Y).

(d) Determine f(x,y), the joint probability density function of (X, Y).