# HW3 - Section 4-2 4-1 a P(1 < X = e x dx =-e x 1 2.5 1 =...

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Section 4-2 4-1. a) 3679 . 0 ) ( ) 1 ( 1 1 1 = = = = < e e dx e X P x x b) 2858 . 0 ) ( ) 5 . 2 1 ( 5 . 2 1 5 . 2 1 5 . 2 1 = = = = < < e e e dx e X P x x c) 0 ) 3 ( 3 3 = = = dx e X P x d) 9817 . 0 1 ) ( ) 4 ( 4 4 0 4 0 = = = = < e e dx e X P x x e) 0498 . 0 ) ( ) 3 ( 3 3 3 = = = = e e dx e X P x x 4-2. a) 10 . 0 ) ( ) ( = = = = < x x x x x e e dx e X x P . Then, x = ln(0.10) = 2.3 b) 10 . 0 1 ) ( ) ( 0 0 = = = = x x x x x e e dx e x X P . Then, x = ln(0.9) = 0.1054 4-10. Because the integral fxdx x x () 1 2 is not changed whether or not any of the endpoints x 1 and x 2 are included in the integral, all the probabilities listed are equal. 4-15. Now, x e x f = ) ( for 0 < x and x x x x x X e e dx e x F = = = 1 ) ( 0 0 for 0 < x. Then, > = 0 , 1 0 , 0 ) ( x e x x F x X 4-29. a) 39 . 109 ln 600 600 ) ( 120 100 120 100 2 = = = x dx x x X E 19 . 33 ) 39 . 109 ln 78 . 218 ( 600 1 600 600 ) 39 . 109 ( ) ( 120 100 1 2 ) 39 . 109 ( 120 100 ) 39 . 109 ( 2 2 120 100 2 2 2 = = + = = x x x dx dx x x X V x x b.) Average cost per part = \$0.50*109.39 = \$54.70

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4-36. min 85 . 1 2 ) 2 . 2 5 . 1 ( ) ( = + = X E 2 2 min 0408 . 0 12 ) 5 . 1 2 . 2 ( ) ( = = X V b) 7143 . 0 ) 5 . 0 )( 7 . 0 / 1 ( ) 7 . 0 / 1 ( ) 7 . 0 / 1 ( ) 5 . 1 2 . 2 ( 1 ) 2 ( 2 5 . 1 2 5 . 1 2 5 . 1 = = = = = < x dx dx X P c.) x x x y dy dy X F
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HW3 - Section 4-2 4-1 a P(1 < X = e x dx =-e x 1 2.5 1 =...

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