5.3 Poisson Distribution

λ

mean number of successes in one interval; Greek letter lambda

For a Poisson random variable X, the probability of obtaining x successes in any particular interval is given by

where x=x= the number of successes, e≈2.718282e≈2.718282, and λ=λ= the mean number of successes in each interval.

The Poisson distribution has the following properties:

1. Each success must be independent of any other successes. 2. The Poisson random variable, X, counts the number of successes in the given interval. 3. The mean number of successes in a given interval must remain constant. 4. For a Poisson distribution, the mean and variance are given by μ = σ^2 = λ, where λ is the mean number of successes in a given interval.

When calculating probabilities for Poisson distributions, round to _ decimal places. This follows the convention used in the Poisson probability distribution tables.

4

Memory Booster

Make sure that your calculation for λλ is in the same unit of measurement as the interval in the question.

The Poisson distribution is

a discrete probability distribution for the number of possible successes over a given interval of time.