Thread: Problem 1.9
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Old 03-16-2017, 10:36 AM
k_sze k_sze is offline
Join Date: Dec 2016
Posts: 12
Default Re: Problem 1.9

Originally Posted by k_sze View Post
So I did end up using moment generating function. And I think the answer to (c) is s = \ln{\frac{\alpha}{1-\alpha}}, using calculus.

But now I'm stuck at (d).

Directly substituting \alpha = \mathbb{E}(u) + \epsilon is probably wrong? Because e^{s}U(s) can be simplified to the point where no logarithm appears (unless I made a really big mistake).

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.

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