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Using R,

Exercise 5 (More Simulation) Let X follow an exponential distribution with rate parameter λ -2. Let Y follow a Poisson distribution with rate parameter Ay 3 We write sd(X) for the true standard deviation of X and m(Y) for the true median of Y Let s be the sample standard deviation of X which is an estimate of sd(X). Also let my be the sample median which is an estimate of m(Y) Suppose we take samples of size n 10 from X and take samples of size ny-5. Consider the statistic

my What is the (sampling) distribution of We could ask a statistician who specializes in theory. Instead olf using mathematics, simulate 5000 times and store the results. Plot a histogram of the observed values of A. Comment on the shape of the histogram and empirical distribution of ^. Before running your code, et the same seed used for the previous exercise. For full credit, do not use a for loop

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