Question

4. -/3 points My Notes Ask Your Teacher 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 X1, X2, and X3 denote the amounts in the selected envelopes, the statistic of interest is M = the maximum of X1, X2, and X3. Obtain the probability distribution of this statistic. (Round your answers to three decimal places.) p(m) 0 0

Answer 1

4. Contains ten Box sealed envelob numbUted 1, 2.. 1O. First six envelop is empty. 5 contai n next too the 10 two contain last the with prco bability = Each envelob is selected P[selected en velop contauns no mouy]= Contains $57 PL selected envetop 17 PE selected 10 cantain envelop at roud om selected CUce 3 envelops NOW i2 1,2,3. in th envelop amount deuote the Xi- maxxiX2,X3Y M = X1Ov KN=0,K X3=0 , means M=0 nos P(M-)= nce there replacement cveut P M2z0) PC30) occLos turefor they cce ind e pendeutn 640 6/10 x10 לו

P CM ) 216 O216 M 5 송 out 아 NoLo, at teaot ay meams . oue 3 selected envelop con tains $5 G=0,X20, x35) o x0X25, x3=0) e(xi5/2- OM2-) TYems (xI5 2O-5 ) (xiso, X2 2 5, pe 5 ,yc0) av :. P(M) P[XI5X2-0 , Xjn0] = 1P Cx=ox2r 0 , M3 = 6) + P I Xi=0 , Xa= 5,x3 e o] + 5, X25 x3-0] + P[XI = 5, X2=0 , X3- 5PEX 2= G/ X$- +fPr 3 X lo 2.62 63 O 288 lo3 + o n 이으

:. P (Heo) 0.216 P (N-5) O.2 88 , P (H 10) 1- 1P0) P(H5) f 2 O.504 1 . o'416, 10 Pm a.216 O:216 O'496 O'288