8. (25 points) Consider a random variable X whose cumulative distribution function is given by 0 if a? 3) : 0.1. (a). (2 points) What is q? (b). (5 points) Compute P(X2 2 > 2). (c). (3 points) What is 10(0)? What is 10(1)? What is p(P(X g 0))? (Here, p(-) denotes the probability mass function (pmf) for X) (d). (5 points) Sketch a plot of the function p(a:) below. (Make sure to label the coordinates on the axes!) (e). (5 points) What is P(2X 3 2 2 | X 2 2.1)? (f). (3 points) Compute E(X). (g). (2 points) Compute E(X2). F(:I:)