Poisson Process Examples

Stochastic ProcessPoisson ProcessDefinition → Example Questions

Following are few solved examples of Poisson Process. You can take a quick revision of Poisson process by clicking here.

Example 1. The number of customers arriving at a rate of 12 per hour. If it follows the Poisson process, then
(a) Find the probability that 4 customers arrive between 9:00 and 9:40
(b) Find the probability that 15 customers arrive between 9:40 and 11:20
(c) Find the probability that 4 customers arrive between 9:00 – 9:40 and 15 arrives between 9:40 – 11:20
(d) Find the probability that 4 customers arrive between 9:00 – 9:40 or 15 arrives between 9:40 – 11:20.

Solution
(a) Here λ = 12 per hour, n = 4 and t = 40 minutes = 40/60 = 2/3 hours
So, by using Poisson process, we have

Poisson Process Examples

(b) Here λ = 12 per hour, n = 15 and t = 1 hour + 40 minutes = 1+(40/60) = 5/3 hours
So, by using Poisson process, we have

(c) Here λ = 12 per hour, and

So, by using Poisson process, we have

(d) Similarly,

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