Question: Derive a likelihood ratio test for the following case. Under hypothesis HI, the observation Z is Gaussian with mean m, and variance cri. Under Ho, Z is Gaussian with mean m« and variance. Find the decision regions as a function of the LRT threshold.
2. Consider the binary symmetric channel shown in Fig. E.3.1, where the transmitted symbols are 0 and 1 and the received symbols are a and
b. E represents the crossover probability [i.e., the probability that the channel output is a(b) when the input is 1(0) and is small]. Obtain a decision rule to minimize the total probability of error if the prior probability of a 1 being transmitted isp. What is the probability of error? Assume that ? <>
