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In: Statistics and Probability

Given two r.v’s X and Y over the same alphabet: (a) Show that the Kullback–Leibler distance...

Given two r.v’s X and Y over the same alphabet:
(a) Show that the Kullback–Leibler distance D(P(X,Y) || P(X) P(Y)) = H(X) – H(X|Y)
(b) Show that the bounds of Mutual Information (MI) are 0 ≤ I(X:Y) ≤ min [ H(X) , H(Y) ]
with equality on the left if and only if X and Y are independent random variables, and
with equality on the right if and only if either Y essentially determines X, or X essentially
determines Y , or both.
(c) Show that the MI is symmetric, i.e. I(X;Y) = I(Y:X)

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orchestra answered 2 years ago
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