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4. (20 points) Calculate the expected value for the following random variables. Show your work and explain each step. (a) Let U be a continuous uniform random variable on [0, 3]. Let X = U3. Calculate E(X). Show all of your work and explain each step. For full credit your final answer should not have any integrals in it. (b) Let Y be a Poisson random variable with parameter ) = 2. Let X = 3 . Calculate E(X). For full credit, your final answer should not include a summation. Show all of your work and explain each step. (c) Let Z be a standard M(0, 1) random variable. Let X = \\Z), the absolute value. Calculate EX. For full credit, your final answer should not include an integral. Show all of your work and explain each step