Question: Show that conditioning reduces entropy, H(YX) Show that conditioning reduces entropy, H(YIX) HO') Specifically, show that on the example of a binary RV X that

Show that conditioning reduces entropy, H(YX)

Show that conditioning reduces entropy, H(YIX) HO') Specifically, show that on the example of a binary RV X that takes values from the set {000, 001 , , 111) with equal probabilities. Evaluate reduction in entropy of X given that it is conditioned on the event A = {X begins with a 1}.

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