hw5sol - ORIE 3500/5500 Fall Term 2008 Assignment...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ORIE 3500/5500 Fall Term 2008 Assignment 5-Solution 1. Let J and F be the number of days with snowfall in January and February. Then J Binomial (31 , 0 . 4) and F Binomial (28 , 0 . 4). (a) P ( J = 4) = ( 31 4 ) 0 . 4 4 0 . 6 27 . i. Since there are 4 Sundays in January, the probability that in all of them there will be snowfall is ( 4 4 ) 0 . 4 4 0 . 6 27 . Hence the required probability is ( 4 4 ) 0 . 4 4 0 . 6 27 ( 31 4 ) 0 . 4 4 0 . 6 27 = 1 ( 31 4 ) . ii. Since there are 8 days which are either Sundays or Saturdays, u sing similar argument as above the required probability is ( 8 4 ) 0 . 4 4 0 . 6 27 ( 31 4 ) 0 . 4 4 0 . 6 27 = ( 8 4 ) ( 31 4 ) . (b) For r = 0 , 1 ,..., 59, P ( J + F = r ) = r X i =0 P ( J = i,F = r - i ) = r X i =0 P ( J = i ) P ( F = r - i ) = r X i =0 ± 31 i ² 0 . 4 i 0 . 6 31 - i ± 28 r - i ² 0 . 4 r - i 0 . 6 28 - r + i = 0 . 4 r 0 . 6 59 - r r X i =0 ± 31 i ²± 28 r - i ² = ± 59 r ² 0 . 4 r 0 . 6 59 - r . 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
(c) For x = 9 , 10 ,..., 28, we have P ( F = x | J + F = 40) = P ( F = x,J = 40 - x ) P ( J + F = 40) = P ( F = x ) P
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/04/2008 for the course STSCI 6000 taught by Professor Turnbull during the Fall '08 term at Cornell University (Engineering School).

Page1 / 4

hw5sol - ORIE 3500/5500 Fall Term 2008 Assignment...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online