Poisson Distribution

• Definition: Models the number of events occurring in a fixed interval of time or space, assuming events occur independently and at a constant average rate $\lambda$
• Mean: $E[X]=\lambda$
• Variance: $Var(X)=\lambda$
• Use case: Count rare events (number of emails per hour, number of accidents per day).

Represented as $\mathrm{Poisson}(\lambda )$