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**Unformatted text preview: **Sixth Homework Set — Solutions Chapter 4 Problem 55 P (no errors) = P (no errors | first typist) P (first typist) + P (no errors | second typist) P (second typist) = 1 2 parenleftbigg 3 0! e- 3 + 4 . 2 0! e- 4 . 2 parenrightbigg = 1 2 ( e- 3 + e- 4 . 2 ) . Problem 57 X is Poisson with parameter λ = 3. (a) P { X ≥ 3 } = 1- P { } - P { 1 } - P { 2 } = 1- e- 3 ( 1 + 3 + 9 2 ) = . 5768 . (b) P { X ≥ 3 | X ≥ 1 } = P { X ≥ 3 } P { X ≥ 1 } = P ( X ≥ 3) 1- e- 3 = 0 . 6070 . Problem 59 Let X be the number of times you win a prize. Then X is binomial with n = 50 and p = 1 100 , i.e., we can use the Poisson approximation with λ = 50 · 1 100 = 1 2 . (a) P { X ≥ 1 } = 1- P { X = 0 } = 1- e- 1 2 = 0 . 3935 (b) P { X = 1 } = 1 2 e- 1 2 = 0 . 3033 (c) P { X ≥ 2 } = 1- P { X = 0 } - P { X = 1 } = 1- e- 1 2 ( 1 + 1 2 ) = . 0902 Problem 61 Let X be Poisson with parameter λ = 1000 · . 0014 = 1 . 4. Then P { X ≥ 2 } = 1- P { X = 0 }- P { X = 1 } = 1- e- 1 . 4 (1+1 . 4) = 0 . 4082 .....

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