Problem 7E

The number of hits on a certain website follows a Poisson distribution with a mean rate of 4 per minute.

a. What is the probability that 5 messages are received in a given minute?

b. What is the probability that 9 messages are received in 1.5 minutes?

c. What is the probability that fewer than 3 messages are received in a period of 30 seconds?

Solution

Step 1 of 4

Here given that the no. of hits on a web site follows the poisson distribution with mean a rate of 4 per minute

Let X is the no. of hits on a web site

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

Then XPoisson(4)

Hence =4