# MAS-I, Mahler 2022 Sample Exam; #14&45

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I’ve primarily been using The Infinite Actuary’s (TIA) seminar to study for Exam MAS-I, but I figured it wouldn’t hurt to try some practice problems & sample exams from other sources… including the one “free” sample exam on Howard Mahler’s website.  I still have quite a few missed questions to review and figure out the source of my error; for now though, there were two in particular I wanted to ask about here.  (I realize the best/simplest solution may be to just email Mr./Prof. Mahler himself and ask.)

1) Question 14 gives you 10 claim amount observations, tells you a Gamma distrib. is fitted using the Method of Moments, and asks for the third moment of the fitted distrib.

I understand the method shown in the answer key (using the Gamma formula for E[X^k] from the tables to determine alpha and theta, then plugging them back into the same formula for E[X^3]).  My confusion comes from an alternate method presented in the TIA seminar, where we’re told that for distributions with more than one parameter, the Method of Moments also gives us E[X^k] = SUM((X_i)^k) / N.  Has anybody else seen this formula used elsewhere?  Or is it possible I’m misinterpreting the TIA slides, and the latter method should only be used to estimate/compute the parameter values rather than the K-th moment itself?

2) Question 45 involves Markhov chains and Actuarial Present Value.  More than anything, I’m not sure I understand what the problem is asking and how the answer key shows it (the PDF link above has the original question on pg 27 and the answer on pg 43).

My interpretation was that we were supposed to compute the probability of each potential oil well state at the end of the year (0.60 for “Gusher”, 0.30 for “Normal”, and 0.10 for “Dry”) – then use those probabilities and the 8% interest rate to discount each state’s profit back one year, ending at an APV of approx \$38,890.  However, the answer key seems to account for the profits made during the year, as well as the long-run probability of any future states…?

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