Question: Let X be an exponential random variable with probability density function pX(x) = 1 3 e x 3 for x 0. Which of the answers

Let X be an exponential random variable with probability density function pX(x) = 1 3 e x 3 for x 0. Which of the answers below is the correct combination of P(2X 2) and Var(2X)?

A. P(2X 2) = 0.2835 and Var(2X) = 36

B. P(2X 2) = 0.4866 and Var(2X) = 18

C. P(2X 2) = 0.5134 and Var(2X) = 9

D. P(2X 2) = 0.1711 and Var(2X) = 1.3333

E. P(2X 2) = 0.2388 and Var(2X) = 0.4444

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