# Minimum expected value over all probability functions

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!

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