Question

A box contains ten sealed envelopes numbered 1,..., 10. The first six contain no money, the next two 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, X, and X, denote the amounts in the selected envelopes, the statistic of interest is M = the maximum of X, Xy, and X3 Obtain the probability distribution of this statistic. (Round your answers to three decimal places.) m 0 10 p(m)

Answer 1

for P(m=0) =P(all three envelop contains no money) =(6/10)³ =0.216

P(m=5) =P(all from 8 envelop which contains at most $5)-P(all three with 0 money) =(8/10)³-0.216=0.296

{m=10)=1-(8/10)³ =0.488

m	0	5	10
p(m)	0.216	0.296	0.488