Problem 8.2 Videos 6.1, 6.2 An X-ray source can be run at two different voltages V, and V1. For any millisecond, the number of photons generated by an X-ray source at voltage V (hypothesis Ho) is a Poisson random variable N with E[N|H) = 20. Under voltage V1 (hypothesis H), the number of photons in any millisecond is a Poisson random variable with E[N]H] = 30. Suppose we have prior probabilities that P[H.] = 0.4, P[H1] = 0.6. Assume we observe the actual number of photons N = n in a millisecond, and you want to decide what voltage the source was using. (a) Find the Maximum Likelihood (ML) decision rule for this problem. (b) Find the Maximum a Posteriori (MAP) decision rule decision rule. (c) Compute the average probability of error of both the ML and the MAP decision rules, assuming the prior statistics provided in the problem. You may leave the answer in terms of summations. Compute the difference in the probability of errors between the two decision rules. Problem 8.2 Videos 6.1, 6.2 An X-ray source can be run at two different voltages V, and V1. For any millisecond, the number of photons generated by an X-ray source at voltage V (hypothesis Ho) is a Poisson random variable N with E[N|H) = 20. Under voltage V1 (hypothesis H), the number of photons in any millisecond is a Poisson random variable with E[N]H] = 30. Suppose we have prior probabilities that P[H.] = 0.4, P[H1] = 0.6. Assume we observe the actual number of photons N = n in a millisecond, and you want to decide what voltage the source was using. (a) Find the Maximum Likelihood (ML) decision rule for this problem. (b) Find the Maximum a Posteriori (MAP) decision rule decision rule. (c) Compute the average probability of error of both the ML and the MAP decision rules, assuming the prior statistics provided in the problem. You may leave the answer in terms of summations. Compute the difference in the probability of errors between the two decision rules