Problem #5 (20 points) - A Stationary Poisson Process

The arrival of men at a certain restaurant follows a stationary Poisson

process with a rate of

9

men per hour and the arrival of women at the

same restaurant also follows a stationary Poisson process with a rate of

6

women per hour. In the next

40

minutes, determine the probability that:

a.)

(5 points)

exactly

5

men and

3

women will arrive,

b.)

(5 points)

exactly

3

men and

5

women will arrive,

c.)

(10 points)

exactly

8

people (men or women) will arrive.