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Unformatted text preview: ⇒ X I ∼ Bin (9 , . 1) and X G ∼ Bin (9 , . 9) 1 (a) P (defendant convicted) = P (convicted  guilty) P (guilty) + P ( convicted  innocent ) P (innocent) = P ( X G ≥ 5) P ( guilty ) + P ( X I ≥ 5) P ( innocent ) = [1P ( X G ≤ 4)](0 . 6) + [1P ( X I ≤ 4)](0 . 4) = 0 . 5998218 (b) P (correct verdict) = P (correct  guilty) P (guilty) + P (correct  innocent) P (innocent) = P ( X G ≥ 5) P ( guilty ) + P ( X I ≤ 4) P ( innocent ) = [1P ( X G ≤ 4)](0 . 6) + P ( X I ≤ 4)(0 . 4) = 0 . 999109 Exercises 3.4, Question 8 (a) (iii) negative binomial distribution with r = 5 and p = 0 . 05. (b) S x = { 5 , 6 ,... } . The pmf of X is given by : P ( X = x ) = ± x1 51 ² (0 . 05) 5 (0 . 95) x5 , x = 5 , 6 ,.... (c) P ( X > 35) = 1P ( X ≤ 35) = 0 . 9709737 by R command below. > 1pnbinom(30,5,0.05) [1] 0.9709737 2 3 4...
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 Spring '00
 Akritas
 Poisson Distribution, Binomial distribution, Discrete probability distribution, Negative binomial distribution, XG

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