X is a random variable with an exponential distribution with rate =2.3. Thus the pdf of X is f(x)=ex for 0x where =2.3. 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 X2.3. 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 1X1.5 e) Calculate the probability that x>1 by using the pexp function f) Calculate the probability that X is at least 0.3 greater than its expected value. Use the pexp function g) Copy your R script for the above into the text box here. -17 Points] Suppose X has a standard normal distribution. The pnorm(), dnorm(), and qnorm() functions should be useful in the following. Remember, if X has a standard normal distribution then E(X)=0 and Var(X)=1. a) What is the expected value of 73X+9 ? b) What is the variance of 73x+9 ? c) Using R, find the expected value of 2x4 ? d) Using R, calculate the probability X>1.03 ) e) Using R, calculate the probability that 1.03t=.75 then what is t ? h) Copy your R script for the above into the text box here