working hours, from 9am to 6pm, the IT Service Desk receives requests for service from

Science at rate 4 per hour, and from Humanities at rate 3 per hour, according to two independent

Poisson processes. For the following questions (except (vii)) write formulas without computing the results

numerically.

(a) What is the distribution of the number of requests that arrive between 2:00pm and 2:30pm?

(b) The rst two requests in the morning came from Science. What is the probability that the third

request is also from Science?

(c) Given that 7 requests arrive between 10am and 11am, what is the distribution of the number of

requests from Science among them? Answer the same question but with the time span from 10am

to 12noon.

(d) Given that 7 requests arrived between 10am and 11am, what is the probability that exactly four of

them arrived between 10am and 10:30am?

(e) Given that 9 requests from Science and 7 from Humanities arrived before the noon, what is the

distribution of the waiting time for the rst request after the noon to arrive? (Ignore that the

workday ends at 6pm.)

(f) It takes on the average 9 minutes to process a request from Science and 10 from Humanities. What

is the expected time the Desk needs to process requests coming from the two faculties during 9

working hours?

(g) What is the approximate probability that there are more than 75 requests during a workday