5. Optical communication channel. Let the signal input to an optical channel be: X = 1 with probability 1 2 10 with probability 1 2. The conditional pmf of the output of the channel Y |{X = 1}?Poisson(1), i.e., Poisson with intensity ? = 1 and Y |{X = 10}?Poisson(10). Show that the MAP rule reduces to: ?XMAP(y) = 1, y

5. Optical communication channel. Let the signal input to an optical channel be: X _ 1 With probability 1 _ 10 with probability 5. The conditional pmf of the output of the channel Y|{X = 1} ~ Poisson(1), i.e., Poisson with intensity A = 1 and Y|{X = 10} ~ Poisson(10). Show that the MAP rule reduces to: , _ 1, y