5. A lazy professor issues a homework according to a Poisson process with it = 4 homeworks/ semester. One semester is assumed to be 100 days. (Arjkelt You may use P(k, t} = for the probability that a Poisson process has k arrivals for the duration of t or P(T1 0) for the probability that the inter-arrival time for the Poisson process is less than t. You may leave the exponential in your answer. (a) What is the probability that the class is homeworkfree during one semester? (b) The professor had issued the rst homework on March 2. What is the probability that the professor (who is totally out-ofmind) issued the second homework before March 9? (c) Now the professor (who continues to be out-ofmind) ips two fair coins every time he makes a homework. If both coins show heads, he issues a computersimulation project. What is the probability that this class has at least one project ' 9 during one semester. _