Problem 2 - Information Theory Consider the following channel 012 07 a) Calculate entropy of X, i.c., H(X) when [p(x1), p(r2) = [0.6,0.4). Give p(r1) and p(x2) that maximize H(X) and the corresponding maximum value of H(Xx). b) Give the matrix of transition probabilities [p(Y|X)]. c) Calculate output probabilities [p(Y)]. d) Give output probabilities so that H(Y) is maximum. For this case, then give equations with which you can calculate p(r) and p(r2). he SNR is 20 dB, whereas channel bandwidth is 30 KHz, e) Calculate Shannon channel capacity in bits/sec. ) The channel capacity of a binary symmetric channel is given by C = 1- H(p), where H(p) = -ploga(p) (1 p) log2(1 p). Calculate C for p = 0, 0.5, and 1. Sketch C as a function of ; (Hint: Use lim,0 T log,(x) = 0.] .