AS/A2 Stats 1 Stats 3

S2 Topic 1: Binomial and Poisson distributions
Use of Poisson tables
You must be able to use statistical tables when working out Poisson probabilities
Poisson cumulative distribution function Below is part of a table showing tabulated values of P(X £ x), where X has a Poisson distribution with parameter l.

Use the options here to practice reading values from the tables. Choose values for n, x and p, and use the tables to find the probability. Then check your answer.

l: 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 x: 0 1 2 3 4 5 6 7 8 9 10 P(X £ x) =

Summary The Poisson distribution has one parameter, l l represents the mean number of occurrances Cumulative probability tables are usually provided in examinations. Typically they cover values of l from 0.5 to 10.0, and values of x from 0 to 22. Probabilities involving other values will need either the formula or approximate methods. To find a particular probability, say P(X=3), you must look up P(X£3) and P(X£2) and subtract A note about graphic calculators A graphic calculator, for example the TI-83 or similar model, can work out Poisson probabilities for you. Suppose that X ~ P(5): P(X=2) is given by poissonpdf(5,2)=.0842243375 P(X £ 2) is given by poissoncdf(5,2)=.1246520195 © MathsNet 2001