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A box contains ten sealed envelopes numbered 1, ..., 10. The first five contain no money, the next three each contains $5, and there is a $10 bill in each of the last two. A sample of size 3 is selected with replacement, and you get the largest amount in any of the envelopes selected. If X1, X2, and X3 denote the amounts in the selected envelopes, the statistic of interest is M = the maximum of X1, X2, and X3. Course Title: Probabilistic Methods for Electrical and Computer Engineering Course Code: CE/EE-302 | 5 a) Find the possible values of the statistic M. b) Obtain the population distribution p(x) for the Xi and display it in a pmf table. c) Obtain the probability distribution p(m) of the statistic M and display it in a pmf table. d) As an alternative solution to c), use a tree diagram and show how to compute the probabilities directly from the tree. e) ser Carry out a simulation experiment to compare the distributions of M for various sample sizes. (Hint: Write a computer program to generate the digits 0-9 from a discrete uniform distribution. Assign a value of x = 0 to the digits 0-4, a value of x = 5 to digits 5-7, and a value of x = 10 to digits 8 and 9. Generate samples of increasing sizes, keeping the number of replications constant, and compute M = max(x1,..., Xn) from each sample.) How does the distribution change as n increases