Exercise 5 For part a, you will need to show both derivations and R code. (you may either attach handwritten work, or type them as comments in R, or write them in markdown) For parts b and c, you need to show R code and output Let X ~ Exp(0 = 3). a) (1 pt) Using the inverse CDF method, generate a random sample of length 100 from X using R commands. Hint: You can generate a random sample of uniformly distributed values, then plug them into your expression for the inverse cdf using vectorized operations! b) (0.5 pt) Plot a histogram of your sample using R. c) (0.5 pt) Calculate the sample mean and sample variance using R