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k_sze · #10 04-01-2017, 08:19 AM

Quote:

Originally Posted by k_sze

*sigh*

I did end up getting $\beta$ by substituting $\mathbb{E}(u) + \epsilon$ for $\alpha$ , but only after simplifying $e^{-s\alpha}U(s)$ all the way down, until there is no more

or $\ln$ , otherwise I get two powers of 2 with no obvious way to combine them.

So now the remaining hurdle is to prove that $\beta > 0$ .

Yay

I finally worked out the proof for $\beta > 0$ . Apparently using Jensen's inequality is supposed to be the simple way, but I simply don't get Jensen's inequality, so I used some brute force calculus (first and second derivatives, find the minimum, etc.)