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 an exponential random variable with parameter (and mean) equal to 1.

Find the MAP estimate of , given that there were exactly 5 blue flashes.