Ared light bulb has been flashing forever, according to a poisson process with rate r. similarly, a blue bulb has been flashing forever, according to an independent poisson process with rate b. let us fix t to be 12 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 t until the first event after t. here, an event refers to either bulb flashing.
2. what is the probability that t belongs to an rr interval? (that is, the first event before, as well as the first event after time t, are both red flashes.)
3. what is the probability that between t and t+1, we have exactly two events: a red flash followed by a blue flash?