q6-9sol

# q6-9sol - Math 218(Spring 2008 Solutions to Quizzes 6–9...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 218 (Spring 2008) Solutions to Quizzes 6–9 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) σ 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 λ = 3 / 6 = 1 / 2 order per minute. Thus, P ( X < 3) = 1- e- 3 λ = 1- e- 3 / 2 = . 7769. (b) E X = 1 /λ = 1 / (1 / 2) = 2 (minutes). (c) σ X = 1 /λ = 2 (minutes)....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

q6-9sol - Math 218(Spring 2008 Solutions to Quizzes 6–9...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online