Example 3 The number of calls received in a telephone exchange follows a Poisson distribution with an average of 10 calls per minute. What is the probability that in one-minute duration

1.   no call is received
2.   exactly 5 calls are received
3.   more than 3 calls are received .

 Solution: Let X be the random variable representing the number of calls received. Given

        where Therefore,

1. probability that no call is received 0.000095
2. probability that exactly 5 calls are received 0.0378
3. probability that more the 3 calls are received 0.9897
   

The Poisson distribution is used to model many practical problems. It is used in many counting applications to count events that take place independently of one another. Thus it is used to model the count during a particular length of time of:

• customers arriving at a service station
• telephone calls coming to a telephone exchange packets arriving at a particular server
• particles decaying from a radioactive specimen