undefined

EXERCISE 2.4 (Poisson parameter estimation. In this erample there are two hypotheses, H = 0 and H = 1, which occur with probabilities PHO) = Po and PH (1) = 1 - Po, respectively. The observable Y takes values in the set of non- negative integers. Under hypothesis H = 0, Y is distributed according to a Poisson law with parameter 1o, i.e. e- (2.35) y! Under hypothesis H = 1, y! Py (1) (2.36) This is a model for the reception of photons in optical communication. (@) Derive the MAP decision rule by indicating likelihood and log likelihood ratios. Hint: The direction of an inequality changes if both sides are multiplied by a negative number. (6) Derive an erpression for the probability of error of the MAP decision rule. EXERCISE 2.4 (Poisson parameter estimation. In this erample there are two hypotheses, H = 0 and H = 1, which occur with probabilities PHO) = Po and PH (1) = 1 - Po, respectively. The observable Y takes values in the set of non- negative integers. Under hypothesis H = 0, Y is distributed according to a Poisson law with parameter 1o, i.e. e- (2.35) y! Under hypothesis H = 1, y! Py (1) (2.36) This is a model for the reception of photons in optical communication. (@) Derive the MAP decision rule by indicating likelihood and log likelihood ratios. Hint: The direction of an inequality changes if both sides are multiplied by a negative number. (6) Derive an erpression for the probability of error of the MAP decision rule