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Section 2

Section 2 - CEE 3040 Fall 2008 Section#2 solutions 1 Devore...

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CEE 3040 Fall 2008 Section #2 solutions 1. Devore 5 th Edition, Section 3.2 #12 on pp. 108 Let X = the number of tires on a randomly selected automobile that are under inflated a.) Which of the following three p ( x ) functions is a legitimate pmf for X ? Why are the other two not allowed? x 0 1 2 3 4 p(x) 0.3 0.2 0.1 0.05 0.05 p(x) 0.4 0.1 0.1 0.1 0.3 p(x) 0.4 0.1 0.2 0.1 0.3 Answer: The second pmf is the only legitimate pmf b.) For the legitimate pmf of part (a), compute: P(2 X 4) Answer: 0.5 P( X 2) Answer: 0.6 P( X 0) Answer: 0.6 c.) Suppose: p ( x ) = c (5- x ) for x = 0, 1, …, 4 What is the value of c ? [ Hint : Σ p ( x ) = 1] Answer: c = 1/15 Counting Problems: 1. A party has 50 persons. 45 of them are boys. 5 are girls. If we select randomly 6 people, a.) What is the probability to have exactly 1 girl? Answer : Pr[Select exactly 1 girl] = 0.384 b.) To have at least 2 girls? Answer : Pr[Select at least 2 girls] = 0.103

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CEE 3040 Fall 2008 2. There are 20 people at a party. a.) If there are 10 men and 10 women, how many pairs (men with women) are there? Answer: # of pairs = 10! 2245 3.63 x 10 6 (Line up women and assign men) b.) If all 20 are men (or women) how many pairs are there?
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