1. The problem statement, all variables and given/known data The problem is attached in the pdf 2. Relevant equations 3. The attempt at a solution I have the solution, I just don't really understand it. In the solution, the author takes the expected value of the negative binomial ( n(1-pi)/pi ) and plugs it into the g'(x) function. Then obviously, if you integrate that, you get the original sinh function, because we defined it that way. I don't get he'd just plug in that function.