The Poisson Distribution


the poisson distribution describes the distribution of events which occur randomly in a continuous interval. e.g. time, length, volume etc. the following conditions must apply:

  • the events occur at random
  • the events are independent of one another
  • two or more events do not occur simultaneously
  • the probability that an event occurs in an interval is proportional to the size of that interval

the poisson distribution has only one parameter and that is λ the average number of occurrences of an event in a given time interval. i.e. a rate.

the mean and the variance of the poisson distribution are both λ

Key Skills

  • calculate poisson probabilities using formulae and tables
  • find means, variances and standard deviation for poisson probability distributions


poisson distributionlambdaindependent eventsmeanvariancestandard deviationexpected value.