Assume we have a single branch of a Rayleigh fading signal and that the average Signal to Noise Ratio (SNR) is 25 dB.

a) Calculate the probability that the instantaneous SNR drops below 10 dB.

b) Repeat the calculation for a number of branches M = 2, 3, and 4.

c) Do increases in branches of diversity follow the law of diminishing returns? Explain why or why not.

(The law of diminishing returns says that you get a smaller and smaller return (benefit) as you invest more and more. An example would be: if you spend $100 on insulating your home, you might save $100 on heating costs. Then if you spend another $100, you might only save $50 (because all the major leaks were sealed using the first $100). If you spend yet another $100, you might get no return or benefit from your investment. So the returns gets smaller and smaller ($100, $50, $0) with each addition of resources. Sometimes the law of diminishing returns holds and sometimes it does not.)