sec_3_1_and_3_2_sol

sec_3_1_and_3_2_sol - APPM 4/5570 Solutions to Problems...

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APPM 4/5570 Solutions to Problems from Sections 3.1 and 3.2 10. a. { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } b. If we take S 1 to be the number in use at station 1 and S 2 to be the number in use at station 2, then the diFerence random variable de±ned as S 1 - S 2 would take on the values {- 4 , - 3 , . . . , 5 , 6 } . c. { 0 , 1 , 2 , 3 , 4 , 5 , 6 } d. { 0 , 1 , 2 } 13. a. P ( X 3) = 0 . 10 + 0 . 15 + 0 . 20 + 0 . 25 = 0 . 70 b. P ( X < 3) = 0 . 10 + 0 . 15 + 0 . 20 = 0 . 45 c. P ( X 3) = 1 - P ( X < 3) = 1 - 0 . 45 = 0 . 55 d. P (2 X 5) = 0 . 20 + 0 . 25 + 0 . 20 + 0 . 06 = 0 . 71 e. P (2 6 - X 4) = P ( - 4 ≤ - X ≤ - 2) = P (2 X 4) = 0 . 20 + 0 . 25 + 0 . 20 = 0 . 65 f. P (6 - X 4) = P ( - X ≥ - 2) = P ( X 2) = 0 . 10 + 0 . 15 + 0 . 20 = 0 . 45 (Regarding (e) and (f), it is easier to think about the lines not in use as 6 minus the number of lines that are in use.) 18. The maximum values of the two rolls is shown in the box in each case listed below. 1 is the maximum in 1 out of the 36 cases, 2 is the maximum in 3 out
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sec_3_1_and_3_2_sol - APPM 4/5570 Solutions to Problems...

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