Thread: Problem 1.9
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Old 04-01-2017, 07:19 AM
k_sze k_sze is offline
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Join Date: Dec 2016
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Default Re: Problem 1.9

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Originally Posted by k_sze View Post
*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 e 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.)
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