Past exam of the communication Theory course of the University of Oxford / 2009 / 1 / a / i / Solution

For finite-valued random vectors, the conditional entropy is the average of the entropies of the conditional distributions:Use $0{\log }_{2}0=0$ and omit zero-probability conditioning events. Equivalently,The base two makes all information quantities measured in bits; changing the logarithm base scales them by a positive constant and preserves the inequalities.