Poisson Distribution

Poisson Distribution

1. The Poisson Model

   • for a distribution to be poisson it must:
     • be random
     • be discrete
     • contain only integers
     • have no limits
     • have a constant average
   • lambda is called the Poisson parameter - when its value is known, the distribution is completely specified

2. Mean, Variance and Standard Deviation

   • if the discrete random variable X has the Poisson distribution with parameter lambda, then the value of lambda has already ben identified as the mean value of X
   • the mean value of X, or E(X), is defined as the sum of x times P(X = x)
   • if X has a Poisson distribution with parameter lambda, then: E(X) = lambda, Var(X) = lambda and standard deviation = square root of lambda

3. independant Poisson Distributions

   • if X and Y are independent random variables with Poisson distributions with parameters lambda 1 and lambda 2, then X + Y has a Poisson distribution with parameter lambda 1 + lambda 2