Ne have an optical communication system consisting of a light emitting diode (LED) sending pulses to a photodetector through an optical fiber. A binary 0 corresponds to the LED turned off, implying the emission of a low number of photons, while a binary 1 corresponds to the LED turned on, implying the emission of a high number of photons. Assume, X is a random variable representing the number of photons counted during a T seconds interval. The low logic level (0) and its corresponding number of photons are described by the conditional probability mass function 15 - for x = 0, 1, .., 14, PX10[X = x|0 was sent] 120 0, otherwise. The high logic level (1) and its corresponding number of photons are described by the conditional probability mass function x +1 for a = 0, 1, ..., 18, Px|1[X = x|1 was sent] 190 0, otherwise. Find the threshold x. that minimizes the probability of error of the decision between bit 0 was sent and bit 1 was sent. Assume P0 was sent = 0.6. !!