1. Entropy of functions of a random variable. Let X be a discrete random variable. Show that the entropy of a function of X is less than or equal to the entropy of X by justifying the following steps: H(X.g(X)) H(X) + H(g(X) | X) H(X,g(X)) H(g(x)) + H(X|g(X)) Thus H(g(X)) ≤ H(X). @H(X); > H(g(X)). (2.1) (2.2) (2.3) (2.4)

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