Question 1: A box contains twelve sealed envelopes numbered 1, ..., 10. The first six contain no money, the next three each contain $5, and there is a $10 bill in each of the last three. A sample of size n is selected without replacement, and you get to keep the sum contained in the n envelopes. Let S = the sum contained in the envelopes. a) Derive the sampling distribution of the statistic S when n = 2. b) Derive the sampling distribution of the statistics when n = 3. c) Carry out a simulation of the sampling distribution of the statistic S, and plot a histogram for n = 2, N = 100,000 iterations. d) Carry out a simulation of the sampling distribution of the statistic S, and plot a histogram for n = 3, N = 100,000 iterations. e) Compare the proportions in your histograms to your results in a) and b)