A box contains ten sealed envelopes numbered 1, ..., 10. The first four contain

Question

A box contains ten sealed envelopes numbered 1, ..., 10. The first four contain no money, the next 'our 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 X_1, X_2, and X_3 denote the amounts in the selected envelopes, the statistic of interest is M = the maximum of X_1, X_2, and X_3. (a) Obtain the probability distribution of this statistic. (Round your answers to three decimal places.) (b) Describe how you would carry out a simulation experiment to compare the distributions of M for various sample sizes. This answer has not been graded yet. How would you guess the distribution would change as n increases? As n, increases, p(M = 0) goes to one, p(M = 10) goes to zero. As n increases, p(M = 0) goes to zero, p(M = 10) goes to one. As n, increases, p(M = 0) goes to zero, p(M = 5) goes to one. As n, increases, p(M = 0) goes to zero, p(M = 10) goes to zero.

Explanation / Answer

Not sure about part b.Sorry!

a,.Possible values of M are: 0, 5, 10.

M = 0 when all 3 envelopescontain 0 money, hence p(M = 0) = (.5)3= .125.

M = 10 when there is a single envelope with $10, hence p(M = 10) = 1 – p(noenvelopes with $10) = 1 – (.8)3= .488.

p(M = 5) = 1 – [.125 + .488] = .387.

So probability distribution is,

Hope this will heloful to you.

m 0 5 10 P(m) 0.125 0.387 0.488

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