Question 5 Generate a random sample of size 500 using the I distribution with shape = 0.1 and rate=0.01. (hint: E(X) 10 e V(X) = 1000) = Plot the denisity of this gamma function in appropriate plot. # Enter the appropriate R command here: Write the R code to generate a sample of 500 observation from this Gamma distribution. #Enter the appropriate R command here: Repeat this procedure 1000 times and for each time compute the sample mean of the obtained sample. #Enter the appropriate R command here: Plot a histogram with the sample means obtained and add normal density of the Central Limit Theorem approximation. #Enter the appropriate R command here: Find the 2.5% and 97.5% quantiles of the sample means. #Enter the appropriate R command here: Obtain the 2.5% and 97.5% quantiles of the Normal distribution with = 10 and = 100. # Enter the appropriate R command here: Comment on your findings.