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I(X;Y )I(X;Y/Z)分）(1. 5

7、证明：I(X;Y) H(X) H(X/Y) H(Y) H(Y/X)

证明：

i 1j 1

nm p(aibj)logp(ai i 1j 1

H(X) H(X)

I(X;Y) p(aibj)log

nm

p(aibj)p(ai)p(bj)

bj) logp(ai)

p(aibj)logp(bjai) logp(bj)

i 1j 1

nm

H(Y) H(Y/X)