Question

Starting at time 0, a red bulb flashes according to a Poisson process with rate ?=1 . Similarly, starting at time 0, a blue bulb flashes according to a Poisson process with rate ?=2 , but only until a nonnegative random time ? , at which point the blue bulb “dies." We assume that the two Poisson processes and the random variable ? are (mutually) independent. Suppose that ? is equal to either 1 or 2, with equal probability. Write down an expression for the probability that there were exactly 3 arrivals during the time interval [0,2] . Q1)Probability that there were exactly 3 arrivals during the time interval [0,2] : Q2)Suppose that ? is an exponential random variable with parameter (and mean) equal to 1. Find the MAP estimate of ? , given that there were exactly 5 blue flashes.

Answer 1