Question: An automatic doorbell system rings a bell whenever it detects someone at the door. The system uses a photo-detector such that if a person is

An automatic doorbell system rings a bell whenever it detects someone at the door. The system uses a photo-detector such that if a person is present, hypothesis H1, the photo-detector output N is a Poisson random variable with an expected value of 1300 photons. Otherwise, if no one is there, hypothesis H0, the photo-detector output is a Poisson random variable with an expected value of 1000. Devise a Neyman-Pearson test for the presence of someone outside the door such that the false alarm probability is α ≤ 10-6. What is minimum value of PMISS?

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