X is a random variable with an exponential distribution with rate = 6. Thus the pdf of X is f(x) = λ e¯x for 0 ≤ x where

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X is a random variable with an exponential distribution with rate = 6. Thus the pdf of X is f(x) = λ e¯x for 0 ≤ x where λ = 6. 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 x2.5 c) Using the dexp function and the R integrate function calculate the expected value of X. d) Using the pexp function find the probability that 0.2 ≤ x ≤ 0.5 e) Calculate the probability that X > 0.79 by using the pexp function f) Calculate the probability that X is at least 0.3 more than its expected value. Use the pexp function g) Copy your R script for the above into the text box here.