The Poisson Probability Distribution

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Presentation transcript:

The Poisson Probability Distribution Properties of a Poisson Experiment The probability of an occurrence is the same for any two intervals of equal length. The occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval. Named after Simeon Denis Poisson (1781-1840) a French mathematician.

The Poisson Probability Distribution Poisson Probability Function where: f(x) = probability of x occurrences in an interval  = mean number of occurrences in an interval e = 2.71828

Example: Mercy Hospital Using the Poisson Probability Function Patients arrive at the emergency room of Mercy Hospital at the average rate of 6 per hour on weekend evenings. What is the probability of 4 arrivals in 30 minutes on a weekend evening?  = 6/hour = 3/half-hour, x = 4

Example: Mercy Hospital Tables of Poisson Probabilities, Appendix B, A-25

Oh! Mercy, not more Poisson?! 6 Arrivals /Hour P(3) in 20 minutes P(1) in 10 minutes P(>1) in 20 minutes P(<6) in 30 minutes