4 Messages arrive to a computer server according to a Poisso

4. Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10 per hour. a. What is the probability that three messages will arrive in 1 hour? b. What is the probability that 6 messages arrive in 30 minutes?

Solution

X = No of arrivals of message is Poisson with mean = 10 per hour

a) Prob that 3 messages will arrive in 1 hour

=P(X=3)

= 0.007566

b) Prob that 6 messages arrive in 30 minutes

For 30 minutes mean rate =5

P(X=6 in 1/2 an hour)

= 0.1462