6. (Generating Random Variables) In this question, you will use MATLAB to generate random variables using the trans- form method. Let U be a uniform random variable from 0 to 1. For n > 0, let {Xilie (1,...,n} be exponential random variables with parameter. Let F(x2) be the cdf of a single exponential random variable. You may use the MATLAB function rand to generate U. (a) Determine the inverse of F(x), i.e. F-(u). (b) Now, you will generate X; by applying F-'(u) on U. For = 0.5, generate n = 5000 exponential random variables and plot a histogram of the points. Compare the histogram to a plot of the pdf of X. (c) For = 0.5, generate n = 5000 exponential random variables and take the average of the random variables. How does it compare to the expecation of X