Question

A university professor observes that the arrival process of students to her office follows a Poisson distribution. Students’ questions are answered individually in the professor’s office. This professor has calculated that the number of students who arrive during the time she is answering the questions of a single student has the following distribution:

Prob{0 students arrive} = 0.45,

Prob{1 student arrives} = 0.40,

Prob{2 students arrive} = 0.10,

Prob{3 students arrive} = 0.05

Using the fact that the traffic intensity ρ is equal to the expected number of arrivals during one service, find the probability of having exactly three students waiting outside the professor’s office.

Answer 1