q6-9sol

q6-9sol - Math 218 (Spring 2008) Solutions to Quizzes 69...

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Unformatted text preview: Math 218 (Spring 2008) Solutions to Quizzes 69 TA: Wei Lin Q6.1. (a) P (0 < X < 1) = Z 1 f ( x ) dx = Z 1 2 25 xdx = x 2 25 1 = 1 25 . (b) P (1 < X < 3) = Z 3 1 f ( x ) dx = Z 3 1 2 25 xdx = x 2 25 3 1 = 3 2- 1 2 25 = 8 25 . (c) E X = Z 5 xf ( x ) dx = Z 5 x 2 25 xdx = Z 5 2 25 x 2 dx = 2 75 x 3 5 = 10 3 . 2. Let X be the daily arrival time in hours after noon, which is uniformly distributed between a = 1 and b = 3 . 5. (a) P (1 < X < 2 . 5) = (2 . 5- 1) / (3 . 5- 1) = 3 / 5. (b) E X = ( a + b ) / 2 = (1 + 3 . 5) / 2 = 2 . 25, that is, 2:15 p.m. (c) X = p ( b- a ) 2 / 12 = ( b- a ) / 12 = (3 . 5- 1) / 12 = . 7217 (hour). 3. (a) Let X be the time between orders. Then X has an exponential distribution with rate = 3 / 6 = 1 / 2 order per minute. Thus, P ( X < 3) = 1- e- 3 = 1- e- 3 / 2 = . 7769. (b) E X = 1 / = 1 / (1 / 2) = 2 (minutes). (c) X = 1 / = 2 (minutes)....
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q6-9sol - Math 218 (Spring 2008) Solutions to Quizzes 69...

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