1 / 8

Statistics

Statistics. 4-5: The Poisson Distribution. Definition. The Poisson distribution is a discrete probability distribution that applies to occurrences of some event over a specified interval . The random variable x is the number of occurrences of the event in an interval.

phila
Download Presentation

Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Statistics 4-5: The Poisson Distribution

  2. Definition • The Poisson distribution is a discrete probability distribution that applies to occurrences of some event over a specified interval. • The random variablex is the number of occurrences of the event in an interval. • The interval can be time, distance, area, volume, or some similar unit.

  3. Formula µx• e -µ P(x) = wheree 2.71828 -Go to dist., then choose poissonpdf on your calculator. x!

  4. Poisson Distribution Requirements • The random variable x is the number of occurrences of an event over some interval. • The occurrences must be random. • The occurrences must be independent of each other. • The occurrences must be uniformly distributed over the interval being used.

  5. The standard deviation is  = µ Parameters • The mean is µ.

  6. Difference from aBinomial Distribution • The binomial distribution is affected by the sample size n and the probability p, whereas the Poisson distribution is affected only by the mean μ. • In a binomial distribution the possible values of the random variable x are 0, 1, . . . n, but a Poisson distribution has possible x values of 0, 1, . . ., with no upper limit.

  7. Poisson as Approximation to Binomial • The Poisson distribution is sometimes used to approximate the binomial distribution when n is large and p is small. Rule of Thumb • n 100 • np 10 Value for μ = n • p

  8. Assignment • Page 213: 1-15 odds • Page 218: 1-12 all

More Related