4. Let X be a random variable with N equiprobable outcomes. a) Describe the optimal binary prefix code for this source (i.e. determine the codeword lengths), and compute the average codeword length L(C). b) Provide an optimal code for N = 9. c) For what values of N does L(C) = H(X)? 5. Find an optimal binary prefix code for the infinite source with probabilities p = 1.9, .09, .009, .0009, ...}