Problem 4 4.5 points possible (graded, results hidden] Regular {not junk) emails arrive at your inbox according to a Poisson process with rate 1"; and junk emails arrive at your inbox according to an independent Poisson process with ratej. Assume both processes have been going on forever. Fix a time t to be 8 o'clock. 1. What is the expected length of the interval that t belongs to? That is, find the expected length of the interval from the last event before it until the first event after 3. Here, an event refers to the arrival of either kind of emails. 2. What is the probability that 1 belongs to an RR interval? [That is, the first event before, as well as the first event after time t, are both regular non-junk emails.) 3. What is the probability that between t and t + 1, that exactly 2 emails, a regular email followed by a junk email, arrive