The number of cars arriving at a given intersection follows a Poisson distribution with a mean rate of 4 per second.

a. What is the probability that 3 cars arrive in a given second?

b. What is the probability that 8 cars arrive in three seconds?

c. What is the probability that more than 3 cars arrive in a period of two seconds?

Solution

Step 1 of 4

Here Given the no. of cars arriving at a given intersection follows a poisson distribution with mean rate of 4 per second

Let X is the no. of cars arriving at a given intersection

The pmf of poisson distribution is P(X)=, X=0,1,2,..............

Then XPoisson(4)

Hence =4