AS/A2 Stats 1 Stats 3

S2 Topic 1: Binomial and Poisson distributions
Poisson probabilites 1
Choose a value for l and the Poisson probabilites will be calculated for a wide range of values of x and a chart of the probability distribution will be displayed. By choosing various values of l, decide how this value affects the shape of the distribution. The mean and variance of the distribution are both l.

l :

Summary The Poisson distribution has one parameter, l l represents the mean number of occurrances The distribution is skewed positively when l is small When l is large, the distribution becomes more symmetric mean = l , variance = l 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