Solve the following problem:
In the communication system shown in Figure , the receiver receives two signals r1 and r2, where r2 is a "noisier" version of r1. The two noises n1 and n2 are arbitrary- not necessarily Gaussian, and not necessarily independent. Intuition would suggest that since r2 is noisier than r1, the optimal decision can be based only on r1; in other words, r2 is irrelevant. Is this true or false? If it is true, give a proof; if it is false, provide a counterexample and state under what conditions this can be true.
