Asst6-suggested

Asst6-suggested - ] ( ) ( ) 2969 . 1 64 19 3 8 1 3 2 3 8 1...

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Statistics 427: Homework # 6 Solutions to Suggested Problems 3.81 a. P(X 10) = F(10;20) = .011 b. P(X > 20) = 1 – F(20;20) = 1 - .559 = .441 c. P(10 X 20) = F(20;20) – F(9;20) = .559 - .005 = .554 P(10 < X < 20) = F(19;20) – F(10;20) = .470 - .011 = .459 d. E(X) = λ = 20, σ X = 472 . 4 = λ P( μ - 2 σ < X < μ + 2 σ ) = P(20 – 8.944 < X < 20 + 8.944) = P(11.056 < X < 28.944) = P ( X 28) - P(X 11) = F(28;20) - F(11;20) = .966 - .021 = .945 3.87 a. For a two hour period the parameter of the distribution is λ = α t = (4)(2) = 8, so P(X = 10) = F(10;8) – F(9;8) = .099. b. For a 30 minute period, α t = (4)(.5) = 2, so P(X = 0) = F(0;2) = .135 c. E(X) = α t = 2 4.5 a. 1 = ( )] () 8 3 3 8 2 0 3 2 0 2 3 ) ( = = = = k k k dx kx dx x f x x f(x) 2.0 1.5 1.0 0.5 0.0 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
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b. P(0 X 1) = ] 125 . 8 1 1 0 3 8 1 1 0 2 8 3 = = = x dx x c. P(1 X 1.5) =
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Unformatted text preview: ] ( ) ( ) 2969 . 1 64 19 3 8 1 3 2 3 8 1 5 . 1 1 3 8 1 5 . 1 1 2 8 3 = = = x dx x d. P(X 1.5) = 1 ] ( ) [ ] 5781 . 1 1 64 37 64 27 3 2 3 8 1 5 . 1 3 8 1 5 . 1 2 8 3 = = = = x dx x 4.10 a. b. 1 1 ) , ; ( 1 = = = = = + k k k k k k x dx x k dx k x f c. P(X b) = k b k k b k k b x dx x k = = + 1 1 1 d. P(a X b) = k k b a k k b a k k b a x dx x k = = + 1 1...
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Asst6-suggested - ] ( ) ( ) 2969 . 1 64 19 3 8 1 3 2 3 8 1...

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