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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