Question

Starting at time 0, a red bulb flashes according to a Poisson process with rate À = 2. Similarly, starting at time 0, a blue bulb flashes according to a

Poisson process with rate i = 1, but only until a nonnegative random time X, at which point the blue bulb "dies." We assume that the two Poisson processes and the random variable X are (mutually) independent. 1. Suppose that X is deterministically equal to 1. What is the expected total number of flashes (of either color) during the interval [0, 2]? Expected total number of flashes: 2. In the time interval [0, X], there are exactly 5 flashes. What is the probability that exactly 2 of them were red? Probability that exactly 2 of the 5 flashes were red

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