Stochastic Process → Poisson Process → Definition → 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

**(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,