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Devore 5thEdition, 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? x01234p(x)0.30.20.10.050.05p(x)0.40.10.10.10.3p(x)0.40.10.20.10.3Only the second p(x) satisfies the following two conditions for a legitimate pmf: 1. ( )0≥xp2. ( )140=∑=xxpb.)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] ( )∑=40xxp= ()()()()()4535251505−⋅+−⋅+−⋅+−⋅+−⋅ccccc= 5c + 4c + 3c + 2c + 1c = 15 c Because = 1, we have c = 1/15 ( )∑=40xxp1
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