Section 6.3Summary

1. The Poisson probability distribution is a discrete probability distribution that is used when observing the number of occurrences of an event within a fixed interval of space or time. The random variable represents the number of occurrences of the event in the interval. The requirements for the Poisson probability distribution are that the occurrences should be (a) random, (b) independent of each other, and (c) uniformly distributed over the given interval.
2. The Poisson probability distribution formula is used to calculate probabilities for a Poisson random variable :
   

3. For a Poisson random variable, the mean is , the variance is , and the standard deviation is .
4. The Poisson distribution may be used to approximate the binomial distribution when the number of trials is large and the probability of success is small.