17s418hw4sol.pdf - Stat 418 HW#4 Problem 4.6 1/8 if X = 3...

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Stat 418 HW #4 Problem 4.6 P ( X ) = 1 / 8 if X = 3 3 / 8 if X = 1 3 / 8 if X = - 1 1 / 8 if X = - 3 Problem 4.7 (a) S = { 1 , 2 , 3 , 4 , 5 , 6 } (b) S = { 1 , 2 , 3 , 4 , 5 , 6 } (c) S = { 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } (d) S = {- 5 , - 4 , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 , 5 } Problem 4.10 Let A be the event that we win something and B be the event that we win i dollars. Then, P ( A ) = 1 / 3 P ( B = 1) = 39 / 165 P ( B = 2) = 15 / 165 P ( B = 3) = 1 / 165 Hence, P ( B = 1 | A ) = 39 / 165 1 / 3 = 117 / 165 P ( B = 2 | A ) = 15 / 165 1 / 3 = 45 / 165 P ( B = 3 | A ) = 1 / 165 1 / 3 = 3 / 165 Problem 4.13 S = { 0 , 500 , 1000 , 1500 , 2000 } 1
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P ( X ) = . 7 × . 4 = . 28 if X = 0 . 3 × . 5 × . 4 + . 7 × . 6 × . 5 = . 27 if X = 500 . 3 × . 5 × . 4 + . 7 × . 6 × . 5 + . 3 × . 5 × . 6 × . 5 = . 315 if X = 1000 . 3 × . 5 × . 6 × . 5 + 3 × . 5 × . 6 × . 5 = . 09 if X = 1500 3 × . 5 × . 6 × . 5 = . 045 if X = 2000 Problem 4.19
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