This is Multimedia and Information Systems question.

4. Consider an alphabet with two symbols A;B, with probability P(A) = x and P(B) = 1-x. (a) Plot the entropy as a function of x. You might want to use log2(3) = 1.6; log2(7) = 2.8. (b) Discuss why it must be the case that if the probability of the two symbols are 1/2+8 and 1/2-E, with small , the entropy is less than the maximum. (c) Generalize the above result by showing that, for a source generating N symbols, the entropy is maximum when the symbols are all equiprobable