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Poisson distribution_mfcs-module 5ppt.pptx
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- 2. POISSON DISTRIBUTION Siméon DenisPoisson (1781–1840)
- 3. Poisson Distribution • Thisis also a discrete distribution. • It was originated by a French mathematician Simon Denis Poisson. • The Poisson distribution is useful for rare events. • In case of binomial distribution , the value of p , q and n are given .since there is certainty of the total no. of events in case of binomial distribution ,so we know the no. of times an event occurs & no. of times ,it doesn’t occur. • But there are cases , where n is large & value of p is very small but such cases arise in case of rare events.
- 6. Poisson Distribution • Conditionsfor Poisson Distribution – Events are discrete (you can count them) – Events can not happen at the same time – An event can occur any number of times during a time period. – Events are independent. In other words, if an event occurs, it does not affect the probability of another event occurring in the same time period. – The rate of occurrence is constant; that is, the rate does not change based on time. – The probability of an event occurring is proportional to the length of the time period. For example, it should be twice as likely for an event to occur in a 2 hour time period than it is for an event to occur in a 1 hour period.
- 7. Poisson Distribution • Assumptionsof Poisson distribution – In the Poisson distribution Size of sample is very large i.e. infinity. – In the Poisson distribution occurrence of event i.e. value of success (p) is approaching zero . – In the Poisson distribution non- occurrence of event i.e. probability of failure (q) is approaching one. – In the Poisson distribution do not know the probability of non- occurrence of an event – The Poisson is the limiting form of binomial distribution as n becomes infinitely large (n >20) and p approaches zero (p < 0.05) such that np = m remains fixed. n is approaching towards infintity.
- 8. Poisson Distribution Examples The Poissondistribution may be useful to model events such as – The number of patients arriving in an emergency room between 10 and 11 pm – The number of laser photons hitting a detector in a particular time interval – Number of phone calls in a day at call centre – Number of print jobs in a minute – Number of mistakes per page committed by a typist. – Number of accidents due to falling of trees or roofs. – Number of goals in games of football or hockey etc. – Number of death in flood – Number of visitors to a web site per minute
- 9. • A classicalexample of the Poisson distribution is given by road accidents. • As we know the number of people travelling on the road is very large i.e., n is large. • Probability that any specific individual runs into an accident is very small. • In all examples ,we know about the happening of an events but we do not know how many times it does not occur . • The reason is that no. of events is very large here and the nature of event is of rare type. • We can know the probability of such rare events by using the poisson distribution.
- 10. Poisson Distribution Applications • Birthdefects and genetic mutations • car accidents • Traffic flow and ideal gap distance • Hairs found in McDonald's hamburgers • failure of a machine in one month • Queuing theory (waiting time problem) • The demand for a product in equal intervals of time. • Arrival Pattern in a departmental store. • The occurrence of defects in a manufacturing units.
- 11. Poisson distribution The followingformula can be used for computation of Poisson probability: x=0,1,2,3… e=2.71828 (but use your calculator's e button) μ or = mean number of successes in the given time interval or region of space . OR
- 12. Examples Example- 5.10 Example- 5.11 Example-5.12 Example- 5.13
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