The arrival rate of customers at a reservation center follows Poisson distribution with a mean of 55 per hour. The service rate of the counter .clerk also follows Poisson distribution with a mean of 65 per hour, (i) What is the probability of having 0 customer in the system? (ii) What is the probability of having 6 customers in the system
Answers
Given : The arrival rate of customers at a reservation center follows Poisson distribution with a mean of 55 per hour. The service rate of the counter .clerk also follows Poisson distribution with a mean of 65 per hour,
To find : What is the probability of having 0 customer in the system? (ii) What is the probability of having 6 customers in the system
Solution:
P(x) = λˣ e^(-λ) / x!
Mean arrival rate of customers λa = 55
Mean service rate of the counter λs = 65
probability of having 0 customer in the system
= 0 customer arrival + 0 Service - ( 0 customer arrival * 0 Service)
55⁰ e⁻⁵⁵ / 0! + 65⁰ e⁻⁶⁵/ 0! - 55⁰ e⁻⁵⁵ / 0! x 65⁰ e⁻⁶⁵ / 0!
= e⁻⁵⁵ + e⁻⁶⁵ - e⁻⁵⁵e⁻⁶⁵
= e⁻⁵⁵ + e⁻⁶⁵ - e⁻¹²⁰
probability of having 6 customers in the system
= (6 service) * ( 6 or more than 6 arriving customers ) + ( 6 Customer arrival) (Service 6 or more than 6 ) - ( 6 customer arrival * 6 Service)
Learn more:
The number of traffic accidents that occur on a particular stretch of ...
https://brainly.in/question/15583001
The number of traffic accidents that occur on a particular stretch of ...
https://brainly.in/question/9077309