Let X be a discrete random variable with PMF p(x), and Y be a continuous random...

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Let X be a discrete random variable with PMF p(x), and Y be a continuous random variable with PDF f(y). (1) Suppose that the values of p(x) are given by the following table: I 0 2 8 p(x) 1/8 2/8 5/8 Find the CDF of X. (2) Find E[Y] if f(y) takes the following form for some constant C: [Cy², 0≤ y ≤1, otherwise. f(y) = Let X be a discrete random variable with PMF p(x), and Y be a continuous random variable with PDF f(y). (1) Suppose that the values of p(x) are given by the following table: I 0 2 8 p(x) 1/8 2/8 5/8 Find the CDF of X. (2) Find E[Y] if f(y) takes the following form for some constant C: [Cy², 0≤ y ≤1, otherwise. f(y) =