26 Jun 2001

Main Points

The Poisson Distribution

A drv X is said to have a Poisson distribution with parameter l (> 0) if its pdf is given by
P(X = x) = e-l
,�� for x = 0, 1, 2, ... .
We write X ~ Po(l).

The Poisson distribution was introduced by S. D. Poisson.

Note that there is no upper limit to the value of x.

Uses of the Poisson Distribution

There are two main uses of the Poisson Distribution.

1.��� It is frequently used when considering the distribution of events which occur randomly in time or space.

2.��� It is used as an approximation to the binomial distribution under situable conditions.

Expectation & Variance

If X ~ Po(l), then E(X) = l, Var (X) = l.

The Recurrence Formula

P(X = x + 1)
P(X = x)
(x + 1)

Two Independent Poisson Variables

If X and Y are independent variables with
X ~ Po(l1) and Y ~ Po(l2),
then X + Y ~ Po(l1 + l2).

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