Probability

The probability that an earthquake occurs is estimated to be 1.5%. If an earthquake occurs, then scientists receive a signal X = 5 + N from a sensor, where N is Gaussian distributed with mean 0 and variance 1. If no earthquake occurs1 then scientists receive a signal X = N. Let the hypothesis Hg be that no earthquake occurs. (:1) Find the ML decision rule and its miss and falsealarm probabilities. (3)) Find the MAP decision rule and its miss and falsealarm probabilities. (c) Find a decision rule that keeps the miss probability equal to or below 0.05%