Can we finally discuss the exam?

[Nonpareil]

OK, are we allowed to discuss exam specifics now? It's 12/8 and after 9 PM EST.

[Moderator1]

Sure. Arlie Proctor, who has or had something to do with the CAS exam structure, said that after 9 PM on 12/8 would be ok.

[Nonpareil]

OK, here goes. I was surprised about the exam. It wasn't exactly what I expected. Most of the questions were on basic topics. There were none of the more exotic distributions - nothing even on lognormal, bivariate normal, or gamma. There were also no questions on Chebyshev or joint transformations on my exam. So in that sense it was easier than I expected. On the other hand, some of the questions were complicated, and many were tricky, requiring that you carefully work through the problem. The expected value was rarely asked for, instead almost always the standard deviation or the variance was required. To me, the exam tested speed and accuracy of calculation, as well as the ability to spot and avoid the potential pitfalls in the some of the problems. Mastery of the material was definitely required, but it was mastery of the basics. Few were straight one-line problems. I was glad I worked so many practice problems and built up my speed. Speed was of the essence for the exam.

I thought the CBT was set up well. I liked how easy it was to go back through the unsolved problems and the ones you had marked. I worked through 24 problems on my first pass in about 1.5 hours, and then went back to the 6 I skipped. I worked through those in about the next 30 or 45 minutes, and spent the last 45 minutes checking my work and making sure I didn't make any mistakes. Most of the questions were a little tricky, and there was usually a short way to work the problem, as well as a long way. I usually found a shorter method the first time through, so the second time I was able to work a different way, giving me a good way to check my work. I only changed my answer on one question, a fairly complicated question about the median of the absolute difference of the pdf values from the pdf median ("median absolute deviation").

[Nonpareil]

I took the exam, Friday, Dec. 1st. FWIW, I didn't like the scrap paper, which I couldn't erase on (and why did it have to be green, was there a sale on green scrap paper?)

Listed below are the problems I recall, as best I recall them, with my solutions, where I recall them. I wrote down as much as I could remember about the test as soon as I got to my car after leaving the exam, otherwise I would be lucky to remember two or three of these. By the way, these are totally out of order compared with the sequence in which they appeared on my exam.

Post edited: too many problems are given, in sufficient detail to get the numerical answer. "Publishing" that much about the test moves from discussion (allowed) to recreating the exam (not allowed). I've chopped it to just #20, leaving that since someone else commented on it. Listing 5 or so should be OK; by deleting all except one christian can choose which ones he considers most interesting. - Mod1


20. Insurance is sold to two territories X and Y and these are the only territories. The probability of no claims for both territories combined = 0.2. The probability of no claim|X = 0.15. The probability of no claims|Y = 0.4. What is the probability that an insurance policy selected at random comes from territory X given that it has no claims?

A: Another Bayes problem with a twist. Using the law of total probability,
P(no claims) = P(no claims and X)+P(no claims and Y) = P(X)P(no claims|X) + P(Y)P(no claims|Y). Since there are only two territories, P(X)+P(Y) = 1 so P(Y) = 1-P(X). Let p = P(X). Then .2 = p(.15)+(1-p). Solving for p yields p = 0.8. Now we can use Bayes : 0.8*.15/(0.8*.15+0.4*0.2) = 0.6.

The other 4 questions involved finding the conditional standard deviation, covariance, variance, or variance of x given y, that sort of thing, all for joint pdfs, typically on the domain 0<y<x<1 (or 0<x<y<1). There were so many of these and they were all so similar that they sort of ran together in my mind.

[ultrafilter]

Yeah, all my questions were on the more normal stuff--no exotic distributions, no order statistics, no joint transformations. I think the two biggest topics were Bayes' theorem and the central limit theorem. Overall it seemed like more of a mental endurance challenge than a test of a deep understanding of the material, but that's what I was expecting.

I finished 24 of the questions in about 2 hours, and then went back and got 5 more of them in the next 30 minutes. The last was some god-awful trivariate distribution where the variables were bounds for each other, and I figured I had the choice of solving that or reviewing all of my other answers. I opted to do the review, and worked a couple of the problems in a different way and got the same answers. I feel pretty good about the exam, but I went ahead and registered for the February sitting just to be safe. If I do have to take it again, I'll be concentrating on my calculus more than anything else.

[Art Vandelay]

My mix of questions was just as Christian described with no "exotic" distributions or joint transformations and involved "mastery of the basics" for the most part. This worked out great for me, becaused I focused much more on working practice problems and doing practice exams simulating exam conditions than worrying about memorizing all of those distributions.

I feel good about how I performed, but I had kind of a rough start. For some reason I was feeling tremendous pressure in the first 20 minutes or so. So much that I felt as if some of the early questions were complete gibberish when I went through the first time. I never really felt pressure in college while taking tests, but I think this exam mattered more to me than any test I had ever taken in my life. I think the CBT had something to do with it as well, since it was such a different feel than using pencil and paper. Also, most of the other test takers in the room were doing some exam that required a ton of typing, so there was loud keyboarding in the background that distracted me at first.

During this time I only managed to answer one out the first five problems, so naturally I was starting to think that I am going down in flames. But then I started getting momentum with the problems afterward and I think I had about an hour left after my first pass through. To my delight when I went back to many of the problems I skipped, they were not gibberish anymore and I answered them confidently. After getting 24 answered confidently, I was running out of time so I guessed on the remaining six that for some reason I had difficulty cracking and spent the rest of the time passing through the 24 I answered quickly making sure that I didn't miss some detail along the way. In my practice exams I would usually miss one or two that I thought I had correct, so hopefully I did no worse than that on the real thing.

[jy006m]

Yeah, my exam was similar where there were no exotic distributions. If I were to estimate how often each topic was tested, I would say 2-3 basic probability, 2-3 bayes, 2-3 uniform, 3-4 exponential, 2-3 poisson, 3-4 binomial, 3-5 normal & central limit, 1-2 single density function, 5-6 joint distributions, 2 single variable transformations, and 1-2 moment generating functions. Negative binomial wasn't even on mine, and Chebyshev didn't show up either.

Before I started the exam, I also noticed that there were people constantly typing, but luckily my test center provided us with earmuffs.

One question that totally caught me off guard was when they asked me to find E(x) given p(x,y) where it was a discrete joint probability function. I had it set up, but I just couldn't figure out how to sum it up.

Overall I answered 24 questions confidently, unsure about 2, and guessed on the remaining 4.

[ba553th0unD]

Thanks for the pretty inclusive review, Christian. I do have a question, though - I thought number 20 asked for "the probability that an insurance policy selected at random comes from territory X AND has no claims?" ("and" and not "given")I might be wrong, but I remember reading the question a couple times over, trying to figure out what exactly was being asked. If that was the phrasing used instead, would the answer change?

[Nonpareil]

Originally Posted by ba553th0unD

Thanks for the pretty inclusive review, Christian. I do have a question, though - I thought number 20 asked for "the probability that an insurance policy selected at random comes from territory X AND has no claims?" ("and" and not "given")I might be wrong, but I remember reading the question a couple times over, trying to figure out what exactly was being asked. If that was the phrasing used instead, would the answer change?

No, I recall my question asked for the probability that it comes from X given no claims. I clearly remember it being conditional. But I could be misremebering the exam. Or there could have been slight variations of this question posted on the exam.

Moderator, I didn't mean to recreate the exam. I thought we could discuss specifics. I'm not sure where the line is. Please advise.

[Moderator1]

The SOA and CAS object to recreating the exam. We have to guess what that means. I suggested you could go ahead and just post 5 more you thought were interesting, or that you didn't know how to do (I don't remember if there were any those). Beyond that posts become a valuable study resource for future exam takers, for maybe seeing exact questions they'll get. Some may go through exam discussions anyway, but it's more work.

If someone else asks about a problem (e.g., "I had this problem about rainfall and I couldn't figure out what to do", you should feel free to say exactly what you thought that problem was and how you did it. That's more discussion of the exam: two people talking about the problem.

That's my opinion. The SOA and CAS may think a little differently, but they've never objected to discussion we've allowed about P. They have told us (the Actuarial Outpost in particular) that recreating the exam is not allowed.