fall 2005 STAT 230 test3soln

fall 2005 STAT 230 test3soln - STAT 230 Test #3 October 25,...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: STAT 230 Test #3 October 25, 2005 4:30 – 5:15 pm 1. During scheduled office hours students come to the Tutorial Centre according to a Poisson process, with an average of one student every three minutes. [4] (a) Find the probability that two or more students visit in a particular 1-minute period. Soln : Let Y be the number of students arrive at the centre in a 1-minute period, then Y ∼ Poisson (1 / 3). P ( Y ≥ 2) = 1- P ( Y = 0)- P ( Y = 1) = 1- exp(- 1 / 3)- (1 / 3)exp(- 1 / 3) = . 045. [4] (b) Suppose we partition an hour into 60 consecutive 1-minute intervals. We call an interval ”Busy” if two or more students arrive at the centre during it. Give an expression for the probability that exactly 3 intervals are Busy in a one-hour period. Soln : This is a Binomial probability with x = 3, n = 60 and p = 0 . 045, i.e., ( 60 3 ) p 3 (1- p ) 57 . [4] (c) Use a suitable approximation to compute the probability in (b). Soln : Since n is big and p is small, the probability in (b) can be approximated by a Poisson probability with μ = np = 2 . 7, i.e., (2 . 7 3 / 3!)exp(- 2 . 7) = 0 . 22....
View Full Document

This note was uploaded on 03/03/2010 for the course STAT 230 taught by Professor Various during the Fall '06 term at Waterloo.

Page1 / 2

fall 2005 STAT 230 test3soln - STAT 230 Test #3 October 25,...

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

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