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answersbookchapter53 - Chapter 5 P1 1 = ∞ R-∞ f x dx =...

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Unformatted text preview: Chapter 5 P1 1 = ∞ R-∞ f ( x ) dx = 1 R- 1 c (1- x 2 ) dx = 2 c 1 R (1- x 2 ) dx = 2 c 2 3 , so c = 3 4 . If x ≤ - 1 then F ( x ) = 0. If- 1 < x < 1 then F ( x ) = x R-∞ f ( t ) dt = x R- 1 3 4 (1- t 2 ) dt = 3 4 ( x- x 3 3 + 2 3 ). If x ≥ 1, then F ( x ) = 1. P6(b) 0 for the symmetry of f . P11 Let X be uniformly distributed on [0 ,L ]. We are looking for P { (( X < L 2 ) and ( X L- X < 1 4 )) or (( L 2 < X ≤ L ) and ( L- X X < 1 4 )) } = P { (0 ≤ X < L 5 ) or ( 4 5 L < X ≤ L ) } = 2 5 . P12 The second case is better. To see this, graph the function g ( x ) where g ( x ) is the distance to the nearest service station and compare the areas under the curves. P13 (a) 2/3 (b) 1/3 P15 Let Z = X- 10 6 . (a) 5- 10 6 =- 5 6 . P { X > 5 } = P { Z >- 5 6 } = P { Z < 5 6 } = Φ( 5 6 ) = . 797. (b) 4- 10 6 =- 1, 16- 10 6 = 1. P { 4 < X < 16 } = P {- 1 < Z < 1 } = Φ(1)- Φ(- 1) = 2Φ(1)- 1 = 2 · . 8413- 1 = 0 . 6826 P16 Let X be the annual rainfall and Z = X- 4 4 ....
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answersbookchapter53 - Chapter 5 P1 1 = ∞ R-∞ f x dx =...

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