Using this information, answer the following questions. Make sure to include all your relevant R code and output. (a) Recall that EXP(9) denotes the exponential distribution with rate parameter A = 9. What is the mean and the variance of this distribution? (2 marks) (b) Suppose that a simple random sample of size n is sampled from this EXP(9) distribution. According to the Central Limit Theorem, if n is sufficiently large then the sample mean estimator is approximately normal in distribution. What is the mean, variance and standard deviation of this approximating normal distribution? (3 marks) (c) Create a histogram in R of n = 100 observations generated from the EXP(9) distribution. Describe the shape of the histogram.