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Section2 - Devore 5th Edition Section 3.2#12(pp 108 Let X =...

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Devore 5 th Edition, Section 3.2 #12 (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 Only the second p(x) satisfies the following two conditions for a legitimate pmf: 1. ( ) 0 x p 2. ( ) 1 4 0 = = x x p b.) For the legitimate pmf of part (a), compute: P(2 X 4) = p(x) + p(3) + p(4) = 0.1 + 0.1 + 0.3 = 0.5 P( X 2) = 0.4 + 0.1 + 0.1 = 0.6 P( X 0) = 1-0.4 = 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] ( ) = 4 0 x x p = ( ) ( ) ( ) ( ) ( ) 4 5 3 5 2 5 1 5 0 5 + + + + c c c c c = 5c + 4c + 3c + 2c + 1c = 15 c Because = 1, we have c = 1/15 ( ) = 4 0 x x p 1
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