More AEP n this problem, we'll continue exploring how interesting limits from the AEP and briefly look at a typical set-influenced coding scheme. a. Suppose we have some sequence of tuples (Xi, Yi) p(x, y) sampled iid from some joint distribution. Find the limit of the likelihood ratio that Xi, Yi are independent. That is, find lim n p(Xn)p(Y n) p(Xn, Y n) . Recall that p(Xn) = p(X1, , Xn) and p(Y n) = p(Y1, , Yn). Hint: AEP can be used for the log likelihood. b. OPTIONAL: Suppose now we have X1, X2, sampled iid from p(x), x Z . Likewise, take another PMF q(x) defined on Z . Show lim 1 n log q(X1, , Xn) = D(p q) H(p) as n . Note: D(p q) P xZ p(x) log p(x) q(x) is defined as the KL divergence between two discrete distributions (as a quasi-distance metric, you can verify D(p p) = 0. To get some more intuition for the typical set, lets consider an example where a source outputs strings of 150 binary digits - for