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Find the minimum value of $E[X]$ over all probability density functions f(x) satisfying the following three constraints:

(I) $f(x) = 0 $ for $x \leq 0$

(II) $ \int_{-\infty}^{\infty} f(x) dx = 1 $

(III) $h(f) = h$

Thanks!

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  • $\begingroup$ Can you elaborate what's $h(f)$ and $h$? $\endgroup$ – Todor Markov Dec 3 '18 at 20:24
  • $\begingroup$ That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional $\endgroup$ – Felipe Dec 3 '18 at 20:48

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