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#1
01-31-2018, 10:32 AM
 verdun11 SOA Join Date: Dec 2015 College: University of North Carolina Posts: 21
SOA 180 Solution Question

In the solution, they use a Gamma integral and what not. I'm a bit confused why. Why didn't they just find the sample variance of the exponential MLE (6^2)/2= 18 and the derivative of the F(x) function (-x/theta^2)*e^(-x/theta), and use 18 * ( (10/6^2)* e^(-10/6) ) ^2 to solve.

What exactly am I missing here with their approach, and is there an easier way to do it than the SOA did?
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#2
01-31-2018, 11:59 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,257

That's what they used. You have the derivative of the product of two terms with theta in them. I do not know of an easier way than what was done here..