X is a random variable with an exponential distribution with rate .1 = 0.? Thus the pdf of X is f{x) = .Fl. 3\" for D E x where .Fl. = DJ. 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 X']-2 . :l c) Using the dexp function and the P. integrate command calculate the expected value of X. :l d) Using the pexp function nd the probability that .33 E X E 1 :l e) Calculate the probability that X := 0.15 by using the pexp function f) Calculate the probability that X is at least 1.5 more than its expected value. Use the pexp function g) Copy your R script for the above into the text box here