# Poisson Distribution

## 1 - Probability for cars to pass through a point on road in a 5-minute period

**Problem**

The number of cars passing a point on a road may be modelled by Poisson distribution. At an average, 4 cars enters the Caibaan Diversion Road in Tacloban City every 5 minutes. Find the probability that in a 5-minute period (a) two cars go past and (b) fewer than 3 cars go past.

## Poisson Probability Distribution

The number of occurrences in a given time interval or in a given space can be modeled using *Poisson Distribution* if the following conditions are being satisfied:

- The events occur at random.
- The events are independent from one another.
- The average rate of occurrences is constant.
- There are no simultaneous occurrences.

The Poisson distribution is defined as

$P(x) = \dfrac{e^{-\mu} \mu^x}{x!}$

where *x* is a discrete random variable

*P*(

*x*) = probability for

*x*occurrences

*μ*= the mean number of occurrences

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