SQU campus is not visited often by the students over the weekends, but some students arrive. Girls arrive at the main gate on Saturday in a Poisson scheme at a rate of 6 per 45 minutes whereas boys arrive at a rate of 1 per 30 minutes.

(a) What is the arrival rate per hour for each group of students?

(b) I also visit campus from time to time on the weekends. For example, three

weekends ago, I came on Saturday at 9:00am in the morning. Calculate the probability

that the next student to arrive after my arrival was a girl, not a boy.

(c) After my arrival at 9:00am (mentioned in part b), what is the probability that

there was at least one student arrival by 9:30am?

(d) If a boy coming from outside stays in campus for an exponential amount of

time 2 hours on the average, can we calculate the probability that there are 5 boys in campus at 12:00pm? If yes, what is it? If not, why not?