Stat400Lec8(Ch2.6)_ans - |^,Mk € ^rh Stat 400 Itrture 8 J...

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: |^,Mk € ^rh Stat 400 Itrture 8 J vr*k5 ba,$n V- t) Review (2.5) o Moment-generating function (r.g.f.) and its proper- ties o Calculating mean and variance through m.g.f. o A note about discrete distribution Today's Lecture(2.6) o Poisson Processes, Poisson distribution. o Mean, variance and m.g.f. of Poisson distribution. o Poisson Approximation to Binomial distribution. St&t 400 [nture 8 Poisson distribution Examples: 1. Number of telephone calls arriving at a switchboard between 3pm and 5pm. 2. Number of defects in a 100-foot roll of aluminum screen that is 2 feet wide. 3. Number of road accidents in a year in US. Poisson Process The Poisson process counts the num- ber of events occurring in a fixed time or space, when r the number of events occurring in non-overlapping intervals are independent. . events occur at a constant average rate of,\ per unit time. . events cannot occur simultaneously. Defini,tion: The random variable X has a Po'isson d;is- tributi,on if its p.m.f. is of the form l@) : #."-^, for r : 0,t,2,... where .\ > 0. 20t2 Vo{l++++ > a l*-,"sa eJ -e)-rt\ f r/ t ./t ,&,) X:-l lof10 Stst 400 lEcture 8 Connections between Poisson process and Poisson distribution Let Xt be the number of events to occur in time t (units). Then Xr - Poisson(.\t), and (.\r), P(Xt : ,) : ";i....
View Full Document

This note was uploaded on 03/14/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

Page1 / 3

Stat400Lec8(Ch2.6)_ans - |^,Mk € ^rh Stat 400 Itrture 8 J...

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