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Unformatted text preview: CHAPTER 4 Section 42 41. a) 3679 . ) ( ) 1 ( 1 1 1 = = = = < âˆž âˆž âˆ« e e dx e X P x x b) 2858 . ) ( ) 5 . 2 1 ( 5 . 2 1 5 . 2 1 5 . 2 1 = = = = < < âˆ« e e e dx e X P x x c) ) 3 ( 3 3 = = = âˆ« dx e X P x d) 9817 . 1 ) ( ) 4 ( 4 4 4 = = = = < âˆ« e e dx e X P x x e) 0498 . ) ( ) 3 ( 3 3 3 = = = = â‰¤ âˆž âˆž âˆ« e e dx e X P x x 47 a) 5 . 2 . 2 ) 50 ( 25 . 50 50 25 . 50 50 = = = âˆ« x dx X P b) x x dx x X P x x 2 5 . 100 2 . 2 90 . ) ( 25 . 50 25 . 50 = = = = âˆ« Then, 2x = 99.6 and x = 49.8. 415. Now, x e x f = ) ( for 0 < x and x x x x x X e e dx e x F = = = âˆ« 1 ) ( for 0 < x. Then,  â‰¤ = , 1 , ) ( x e x x F x X 421. < â‰¤ < < = 9 4 , 04 . 4 , 2 . ) ( x x x f Section 44 425. 4 5 . 1 5 . 1 ) ( 1 1 1 1 4 3 = = = âˆ« x dx x X E 6 . 5 5 . 1 5 . 1 ) ( 5 . 1 ) ( 1 1 5 1 1 1 1 4 2 3 = = = = âˆ« âˆ« x dx x dx x x X V 429. a) 39 . 109 ln 600 600 ) ( 120 100 120 100 2 = = = âˆ« 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 = = + = = âˆ« âˆ« x x x dx dx x x X V x x b.) Average cost per part = $0.50*109.39 = $54.70 Section 45 433. a) E(X) = (1+1)/2 = 0, 577 . , 3 / 1 12 )) 1 ( 1 ( ) ( 2 = = = x and X V Ïƒ b) x x t dt x X x P x x x x = = = = < < âˆ« ) 2 ( 5 . 5 . ) ( 2 1 Therefore, x should equal 0.90. c) 0, 1 ( ) 0.5 0.5, 1 1 1, 1 x F x x x x <  = + < 437. a) The distribution of X is f ( x ) = 100 for 0.2050 < x < 0.2150. Therefore, â‰¤ < â‰¤ < = x x x x x F 2150 . , 1 2150 . 2050 . , 50 . 20 100 2050 . , ) ( b) 25 . ] 50 . 20 ) 2125 . ( 100 [ 1 ) 2125 . ( 1 ) 2125 . ( = = = F X P c) If P(X > x) = 0.10, then 1  F(X) = 0.10 and F(X) = 0.90. Therefore, 100x  20.50 = 0.90 and x = 0.2140. d) E(X) = (0.2050 + 0.2150)/2 = 0.2100 Î¼ m and V(X) = 2 6 2 m 10 33 . 8 12 ) 2050 . 2150 . ( Î¼ Ã— = 2 (253 247 1) 1 12 4 + = Section 46 445. a) P(X < 13) = P(Z < (13 10)/2) = P(Z < 1.5) = 0.93319 b) P(X > 9) = 1  P(X < 9) = 1  P(Z < (9 10)/2) = 1  P(Z <  0.5) = 0.69146. c) P(6 < X < 14) = P Z 6 10 2 14 10 2 < < = P( 2 < Z < 2) = P(Z < 2)  P(Z <  2)] = 0.9545. d) P(2 < X < 4) = P Z 2 10 2 4 10 2 < < = P( 4 < Z <  3) = P(Z <  3)  P(Z <  4) = 0.00132 e) P( 2 < X < 8) = P(X < 8)  P(X <  2) = P Z P Z <  < 8 10 2 2 10 2 = P(Z <  1)  P(Z <  6) = 0.15866....
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This note was uploaded on 11/05/2008 for the course EGN 3443 taught by Professor Unknown during the Fall '08 term at University of South Florida.
 Fall '08
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