Briefly discuss the relationship between the Poisson distrib

Briefly discuss the relationship between the Poisson distribution and exponential distribution and provide an example.

Solution

Poisson distribution shows the probability of a given number of events occurring in a fixed interval of time. Example; if average of 5 cars are passing through in 1 minute. probability of 4 cars passing can be calculated by using Poisson distribution.


Exponential distribution shows the probability of waiting times between occurrences of events.
If we use the same example; probability of a car coming in next 40 seconds can be calculated by using exponential distribution.


-Poisson : probability of x times occurrence
-Exponential : probability of waiting times between events.