Question: X is a random variable with an exponential distribution with rate 1 = 0.2 Thus the pdf of X is f(x) = 1 ex for

X is a random variable with an exponential distribution with rate 1 = 0.2 Thus the pdf of X is f(x) = 1 ex for 0 s x where 1 = 0.2. a) Using the f(x) above and the R integrate function calculate the expected value of X. b) Using the f(x) above and the R integrate function calculate the expected value of X0.8 c) Using the dexp function and the R integrate command calculate the expected value of X. d) Using the pexp function find the probability that .67 s X S 2 e) Calculate the probability that X > 3.1 by using the pexp function f) Calculate the probability that X is at least 2.4 less than its expected value. Use the pexp function

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