3. [18] Given two probability distributions p(x) and q(x), their KullbackLeibler distance is defined as DL(p, q)
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3. [18] Given two probability distributions p(x) and q(x), their Kullback–Leibler distance is defined as DL(p, q) := E(p log p
q
). (2.3.105)
Prove that DL(p, q) ≥ 0. Suppose we define the symmetric function S(p, q) := DL(p, q) +
DL(q, p). Is this a metrics?
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