Question: (17 points) Let X be the random variable whose CDF is given by Fx (20) = - ce-Xx x20 otherwise, where > > 0 is

(17 points) Let X be the random variable whose CDF is given by Fx (20) = - ce-Xx x20 otherwise, where > > 0 is a parameter. Then X is an exponential random variable. (a) (2 points) Find c. (b) (2 points) Sketch Fx. (c) (2 points) Find fx, the PDF of X. (d) (2 points) Find P(X E [1, 10]). (e) (1 point) Find P(X 20}). (g) (3 points) Find the median of X. (h) (3 points) Find a formula for the a-quantile value of X, for a E [0, 1]

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