ChapterSolutions - 8 - Chapter 8 Problems 1. 2. Pcfw_0 X 40...

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Chapter 8 133 Chapter 8 Problems 1. P {0 X 40} = 1 P { X 20 > 20} 1 20/400 = 19/20 2. (a) P { X 85} E [ X ]/85 = 15/17 (b) P {65 X 85) = 1 P { X 75 > 10} 1 25/100 (c) n n X P n i i 25 25 5 75 / 1 > = so need n = 10 3. Let Z be a standard normal random variable. Then, > = 5 75 / 1 n i i n X P P { Z > n } .1 when n = 3 4. (a) 15 / 20 15 20 1 > = i i X P (b) > = > = = 20 1 20 1 5 . 15 15 i i i i X P X P > 20 20 5 . 15 Z P = P { Z > 1.006} .8428 5. Letting X i denote the i th roundoff error it follows that = 50 1 i i X E = 0, Var = 50 1 i i X = 50 Var( X 1 ) = 50/12, where the last equality uses that .5 + X is uniform (0, 1) and so Var( X ) = Var(.5 + X ) = 1/12. Hence, { } 3 > i X P P { N (0, 1) > 3(12/50) 1/2 } by the central limit theorem = 2 P { N (0, 1) > 1.47 = .1416 6. If X i is the outcome of the i th roll then E [ X i ] = 7/2 Var( X i ) = 35/12 and so =
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ChapterSolutions - 8 - Chapter 8 Problems 1. 2. Pcfw_0 X 40...

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