Poisson Distribution

Probability · Axiom Academy

Counting rare events in a fixed interval of time or space A random variable X follows a Poisson distribution with parameter λ if: Events occur independently in a fixed interval Events happen at constant average rate λ X counts the number of events in that interval Parameter: λ > 0 (average rate) The PMF has an elegant exponential form: 3. Expected Value and Variance The Poisson distribution has a unique property where the mean equals the variance: E[X] = λ: The average number of events equals the rate parameter Var(X) = λ: The variance also equals λ This property uniquely characterizes the Poisson distribution

This is the written version of the interactive lesson above. See the full Probability course.