Please answer all parts

2) Suppose that you are the student assistant of a course. The tasks you are responsible arrive in accordance with a Poisson Process with mean 4 tasks/day. With probability 0.25 the new task is of type HW and with 0.75 it is of type Mail. The completion time of each task follows an exponential distribution with rates 2 tasks/day and 3 tasks/day respectively. Assume that you process tasks by first come first served strategy and you don't start the next one until the current one has finished. Currently it is Monday 00:00 AM, and you have no unfinished tasks. (a) What is the probability that you will not receive any new HW tasks on Tuesday? (b) Given that today there were 2 mail tasks until 16:00, what is the probability that you will receive exactly 4 mail tasks until the end of today? (c) Suppose on Monday you have received 2 HW and 3 Mail tasks. What is the probability that HW tasks have arrived in the first half of the day and Mail tasks have arrived in the second half