Question: Let f(x) and g(x) be probability density functions. Then show that the following inequality holds Z R f(x) log f(x) g(x) dx

Let f(x) and g(x) be probability density functions. Then show that the following inequality holds Z

R f(x) log

½

f(x)

g(x)

¾

dx ≥ 0, and that the equality holds if and only if f(x) = g(x) a.e.

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