Question

My Notes 4. -13 points 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.) 10 m p(m)

Answer 1

Solution :

m	0	5	10
p(m)	0.216	0.296	0.488

P(x) P(2020) - G=0.6 (1=5) - 2012 P(2=10) = 2 = 0.2 mzo P/M=0) - Plo,o,0) = 0.6 0.6 0.6 - 0.216 P(M=5) - P10,0,5) + p10,5,0+P (5,0;0)+p/0,5,5+ P(5,0,5) +P15,5,0) +P/5,5,5) -10.6*0.6*0-2) + 0.6* 0-2 0-6) + 0-2 *0.640.6) + (0.6 0.2 0 2) + (0.220 6*0.2) + (0.24 0.24 0.6) + (0.2² 0.240.2)

0.072 +0.072 +0.024 +0.024+0.024+ - p(M=5) = 0.072 + 0.296 0.008 PIM=lo) - P(0,0,10) + P(0,5, 10)+ P(0,10,10) +P|0,10,5 )+P(0,100) + P 5,0,10) +P15,10,0)+p(5,5,10)+p/5,10,5) + Pl5,10,16) +p(10,0,0) + P(10,0 10)+1/10, 0,5) + P(10,5,0) + P/10,5,5). +P (10,5, 10) + p ( 10, 10,5) + P(10,10,0) + ( 10, 10, 10 = (0.6*0.6*0.2)+(0.6*0. 20-2) + (0.6*0. 240-2) + (0.640.2 * 0-2) 6.6%0.2 0.6) + €0.2 0.6+0.2 + (0-240-2 * 0-6) + ---1-020 2702 216 - 0.216 + 0 + 0.056 -0.488