Consider a photodetector in an optical communications system that counts the number of photons arriving during a certain interval. a user conveys information by switching a photon transmitter on or off. assume that the probability of the transmitter being on is p. if the transmitter is on, the number of photons transmitted over the interval of interest is a poisson random variable θ with mean λ, and if it is off, the number of photons transmitted is 0. unfortunately, regardless of whether or not the transmitter is on or off, photons may be detected due to "shot noise". the number n of detected shot noise photons is a poisson random variable n with mean µ, independent of the transmitted photons. let t be the number of transmitted photons and d be the number of detected photons. find l[t | d]