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Unformatted text preview: ECI 114 2011fall HW2 solution; due Oct.12, 2011 5pm Q1. a. 130 , 53 2 * 3 * 4 * 5 21 * 22 * 23 * 24 * 25 25 5 = = C b. 1190 17 * ! 4 ! 4 ! 8 17 1 8 4 = = C C c. Let D be the number of defective buses falling into the sample of 5. 022 . 53130 1190 ] 4 Pr[ 25 5 17 1 8 4 = = = = C C C D d. Pr[ D ≥ 4] = Pr[ D =4] + Pr[ D =5] = 023 . 53130 ! 5 ! 3 ! 8 022 . ] 4 [ 25 5 8 5 = + = + = C C D P It might have been tempting to answer with 028 . 21 ] 4 Pr[ 25 5 8 4 = × = ≥ C C D , the idea being that there are 8 4 C ways to choose 4 defective buses out of the 8, and for each one of those ways, there are 21 ways to choose the remaining bus out of the remaining 21, where the 5 th bus could be either defective or nondefective. Obviously both answers cannot be right. The reason this answer is wrong is that it counts certain outcomes (specifically, the ones where all 5 buses are defective) 5 times too often (if you multiply Pr[D=5] above by 5, and add it to Pr[D=4], you’ll get 0.028). For example suppose buses 18 are defective. The sample of buses {1, 2, 3, 4, 5} will appear 5 times among the 8 4 C × 21 outcomes in the numerator above: When {1, 2, 3, 4} appears among the 8 4 C possible selections of 4 buses out of 8, bus 5 will be among the 21 remaining possibilities. When {1, 2, 3, 5} appears among the 8 4 C possible selections of 4 buses out of 8, bus 4 will be among the 21 remaining possibilities. When {1, 2, 4, 5} appears among the 8 4 C possible selections of 4 buses out of 8, bus 3 will be among the 21 remaining possibilities, and so on for leaving buses 2 and 1 out of the group of 4, respectively. Q2. First, we define the events, A: the first card is a black jack (i.e. a jack of spades or jack of clubs) B: the second card is a 10 or an ace C: the third card is greater than 2 but less than 8 So the event “the first card is a black jack; the second card is a 10 or an ace; and the...
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This note was uploaded on 01/19/2012 for the course ECI 114 taught by Professor Mocktarian during the Fall '08 term at UC Davis.
 Fall '08
 Mocktarian

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