[27]

(a) Show that the mutual information I(x; y) = K(x) +

K(y) − K(x, y) according to Equation 3.20 on page 253 is symmetric:

I(x; y) = I(y; x).

(b) Show that the mutual information in Item

(a) coincides with the mutual information I(x : y) = K(y)−K(y|x) according to Equation 3.15 on page 249 up to an O(log K(x) + log K(y)) additive term.