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 (so we have a random sample), 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.
a. Obtain the probability distribution of this statistic.
b. Describe how you would carry out a simulation experiment to compare the distributions of M for various sample sizes. How would you guess the distribution would change as n increases?
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