400Hw08 - STAT 400 Spring 2011 Homework #8 (due Thursday,...

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STAT 400 Spring 2011 Homework #8 (due Thursday, March 17, by 4:30 p.m.) No credit will be given without supporting work. 1. Dick and Jane have agreed to meet for lunch between noon (0:00 p.m.) and 1:00 p.m. Denote Jane’s arrival time by X, Dick’s by Y, and suppose X and Y are independent with probability density functions ( ) = otherwise 0 1 0 3 2 X x x x f ( ) = otherwise 0 1 0 2 Y y y y f Find the probability that Jane arrives before Dick. That is, find P ( X < Y ). 2. Suppose Jane has a fair 4-sided die, and Dick has a fair 6-sided die. Each day, they roll their dice (independently) until someone rolls a “1”. (Then the person who did not roll a “1” does the dishes.) Find the probability that … a) they roll the first “1” at the same time (after equal number of attempts); b) it takes Dick twice as many attempts as it does Jane to roll the first “1”; c) Dick rolls the first “1” before Jane does. 3.
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400Hw08 - STAT 400 Spring 2011 Homework #8 (due Thursday,...

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