Poisson Distribution

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.
 

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

where x is a discrete random variable