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Problem 5, Light Bulbs 3 points possible (graded, results hidden) A red light bulb has been ashing 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 I to be 12 o'clock. 1. What is the expected length of the interval that! belongs to? That is, find the expected length of the interval from the last event before it until the rst event after I. Here, an event refers to either bulb ashing. 2 What is the probability that I belongs to an RR interval? (That is, the rst 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 ash followed by a blue flash