Homework3Solution

Homework3Solution - Homework 3 Solutions July 19, 2007 p187...

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Homework 3 Solutions July 19, 2007 p187 21, 76, 77 p197 6, 7, 10, 27 1. #21 (a) E [ X ] should be larger than E [ Y ] because whereas the bus driver is equally likely to be from any of the 4 buses, the student selected is more likely to come from a bus carrying a large number of students. (b) E [ X ] = 40 148 40 + 33 148 33 + 25 148 25 + 50 148 50 = 39 . 28. E [ Y ] = 1 4 (40 + 33 + 25 + 50) = 37. 2. #76 Let E R be the event that the right box is empty and there are k matches in the left box. For the event E R to occur, the discovery that the right box is empty must be made on the ( N 1 + N 2 - k + 1)th trial. Then P ( E R ) is given by ± N 1 + N 2 - k N 1 ² 1 2 N 1 1 2 N 2 - k * 1 2 . The calculation for E L , the event that the left box is empty and there are k matches in the right box, is calculated similarly. The total probability is given by ± N 1 + N 2 - k N 1 ² 1 2 N 1 1 2 N 2 - k 1 2 + ± N 1 + N 2 - k N 2 ² 1 2 N 2 1 2 N 1 - k 1 2 .

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This note was uploaded on 11/15/2008 for the course STATS 116 taught by Professor Staff during the Summer '07 term at Stanford.

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Homework3Solution - Homework 3 Solutions July 19, 2007 p187...

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