Show R code X is a random variable with an exponential distribution with rate 𝜆 = 6. Thus the pdf of X is f(x) = 𝜆 e−𝜆x

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X is a random variable with an exponential distribution withrate 𝜆 = 6. Thus the pdf of X is f(x) =
𝜆 e−𝜆x
for 0 ≤ x where 𝜆 = 6.a) Using the f(x) above and the R integrate function calculate theexpected value of X. b) Using the f(x) above and the R integrate function calculate theexpected value of
X2.5
. c) Using the dexp function and the R integrate function calculatethe expected value of X. d) Using the pexp function find the probability that0.2 ≤ X ≤ 0.5 e) Calculate the probability that X > 0.79 by using the pexpfunction f) Calculate the probability that X is at least 0.3 more than itsexpected value. Use the pexp function