Assume that the number of network errors experiences in a da

Assume that the number of network errors experiences in a day in a local area network (LAN) is distributed as a Poisson random variable. The mean number of network errors experienced in a day is 1.8.

What is the probability in any given day zero network errors will occur?

What is the probability that in any given day exactly one network error will occur?

What is the probability that in any given day fewer than three networks will occur?

Solution

lamda= 1/1.8

probability in any given day zero network errors will occur =P( X=0)= exp(-lamda)*lamda^0/0!=0.5738

probability that in any given day exactly one network error will occur= P( X=1)= exp(-lamda)*lamda^1/1!

                                                                =exp(-lamda)*lamda/1

                                                               = 0.3188

probability that in any given day fewer than three networks will occur=P( X <3)

                                      =P(X=0)+P( X=1)+P( X=2)

P( X=2) = exp(-lamda)*lamda^2/2! = 0.0885

probability that in any given day fewer than three networks will occur=0.5738+0.3188+0.0885= 0.9810