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Stat400Lec8(Ch2.6) - Stat 400 Lecture 8 Spring 2012...

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Unformatted text preview: Stat 400 Lecture 8 Spring 2012 Review (2.5) • Moment-generating function (m.g.f.) and its proper- ties • Calculating mean and variance through m.g.f. • A note about discrete distribution Today’s Lecture(2.6) • Poisson Processes, Poisson distribution. • Mean, variance and m.g.f. of Poisson distribution. • Poisson Approximation to Binomial distribution. 1 of 10 Stat 400 Lecture 8 Spring 2012 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 • the number of events occurring in non-overlapping intervals are independent. • events occur at a constant average rate of λ per unit time. • events cannot occur simultaneously. Definition: The random variable X has a Poisson dis- tribution if its p.m.f. is of the form f ( x ) = λ x x ! e- λ , for x = 0 , 1 , 2 , ··· where λ > . 2 of 10 Stat 400 Lecture 8 Spring 2012 Connections between Poisson process and Poisson distribution Let X t be the number of events to occur in time t (units)....
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Stat400Lec8(Ch2.6) - Stat 400 Lecture 8 Spring 2012...

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