). Let A E (U, 00). The distribution function of X is given by F(:r) = l eXp()\\\\/E), :1: > 0. (3) Find the inverse function of F(;1'?)., i.e., a: : F 1(a) for O S a g l. (b) Suppose a random variable U N uniform distribution U(U, 1), show that X = F 1(U) follows the distribution F(3:). (c) Write an R program to generate a random sample of size N Sim = 104 from the distribution F(:r) using the inversion method when /\\ = 4. In your R program, set random seed at a xed value by using the R. function set. seedC). To summarize your simulated sample, calculate the sample mean X and sample variance 82 and report them: also draw the histogram of the sample and