Please must be done on R script

X is a random variable with an exponential distribution with rate A = 6. Thus the pdf of X is f(x) = 11 e'b' for O S x where A = 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 nd the probability that 0.2 S X S 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 :]