H3

If X; ~ Exponential()), i = 1, . .. ,n are independent, then Y = X; ~ Gamma(n, A). i=1 (a) Generate 1000 Gamma (5, 2) random numbers using the gamma random number gener- ator in R, and plot them. Find the mean and variance. (b) Generate 1000 Gamma(5, 2) random numbers using the exponential random number generator in R, and plot them. Find the mean and variance. Hint: Use the fact that Exponential()) = Gamma(1, A).] (c) Compare the results from parts (a) and (b) using Q-Q plot