Rayleigh Mixture (20 points) We are given that two RVs u, v are IID with a common Rayleigh Distribution, each RV u, v satisfies the PDF p(r) = 2r exp(-p2), r > 0 = This RV has E[rº] = 1, the average power is normalized to one. The mean value is 1/2 Let n € {0,1}, P(n = 1) = p, be independent of u, v. This Bernoulli RV can be thought of as a random switch. = (a) (5 points) Determine P[u > u] (b) (5 points)Determine P[u? < 6] (c) (5 points)Determine the median of u, that value, so that P[u > U.] = P[u