#1.Calculating the probability distribution of a statistic.

Suppose a box contains ten sealed envelopes numbered from 1 to 10.Envelopes 1 through 5 contain no money.The next three each contain $5, and the last two each contain $10.Reyna selects a random sample of size 3, with replacement.She gets to keep the largest amount in any of the envelopes selected.If1,2, and3 denote the amounts in the selected envelopes, the statistic that captures this situation is, the maximum of1,2, and3

a.Obtain the probability distribution of this statistic.

b.Determine the expected value of this statistic.

c.Suppose we increase the sample size, to be greater than 3.What happens to the probability distribution asincreases?You do not have to prove your answer mathematically, but state your prediction and explain your answer.