What worked, What didn’t

Studying the Easy Stuff

I didn’t spend enough time with the “easy” stuff. On the exam, the problems surrounding the algebra of events were real chestnuts. Likewise, the first time that I took the exam I encountered an “easy” normal curve problem with a clever twist of algebra. This time, there were two normal distribution problems with the same difficult twist. Study the easy stuff.

One and a Half Years of Study

Actually, two winters worth of studying. My first winter of studying suffered from a lack of study materials. The only book that I had was the free Finan book, plus whatever statistics books were on my shelf (Hogg and Tanis, Casella and Berger). I mostly worked problems from the Online Math Tests Home Page. This was not nearly enough of a variety of problems. Also, my first crack at studying required much reviewing of calculus topics.

The second winter worth of studying was more varied, and more productive. For me, one and a half years was just the right amount of study time. (During this same period, I also bought and renovated a dilapidated house, worked lots of 55 hour weeks at my job, had major surgery, and was reasonably available for my friends, family, pets, and spouse.) For exam FM, I am planning 1 year.

Actex Manual (Broverman)

The exercises in this book are difficult and varied. I will get the Actex manual for FM.

Guo Book

This book provided me with some variety of material when I needed it, and got me thinking about highly efficient solutions. I may get the book for FM.

Finan Book

This book was a good start for me. There are no worked solutions for the exercises, which can become frustrating. I am now started on the book for FM.

Coaching Actuaries

This was a great help at the last minute, in getting a feel for the real test. For the next exam, I am going to get a one month subscription, two months before my exam.

Having Some Background with the Material

Thinking that I had some sort of familiarity with probability was a handicap for the first exam. It encouraged me to not be as thorough with the “easy” stuff as I should have been.

Fortunately, for exam FM/2, I will not have the same problem. I have no background with the material, so I am starting everything from the beginning.


My memory work deserves some real thought, and a post of its own, to follow later.

In short, I am glad that I put as much time as I did into memory work, although it is hard to place its role in passing the exam. The biggest payoff is in the work that I performed in turning complex topics into little digestible examples. As a result, the elementary distributions now have a permanent place in my consciousness.

Early Mornings

Early mornings work for me. I stuck with a wake up time of 3:30 am, or at latest 4:30 am, for more than 6 months. I had time each mornings to complete the most important study tasks, so any additional study time after work was bonus study time. I could study in the afternoons in the coffee shop, and not worry if I lost some study time in socializing


Never in my life have I been so stressed, terrified, and nervous.

Registering, in the testing center, I had trouble following the simple instructions: signing my name, turning this way or that for the metal detector, pulling out my drivers license.

During the test, I felt as if I missed over half the problems. My thinking was very unclear. Unfamiliar problems were absolutely daunting, calculation-intense problems were like Mount Fuji, and questions that involved extra logical twists were like cinder block walls.

When the exam results appeared on the screen, I did not understand the words.

Back out in the registration room, I was just as nervous as before the exam. I could not figure out how to hand my scrap paper and pencils to the gentleman behind the counter. I dropped things. I spoke in garbled syllables.

In my car, I balled for a few minutes, then laughed hysterically, then balled some more. I still couldn’t shake all of the nervousness off.

But I passed.

9 more Days.

I thought that I was studying intently before, but now I am really studying.

A week back, I signed up to take mock exams from Coaching Actuaries.  I have been taking one or two exams each day, plus reviewing answers.  This study choice was a very good one right now.  I have a much better feel for what I can accomplish with two or three hours of intense concentration.

It has been especially satisfying to successfully solve problems of types I have never before seen.  That is the fruit of hundreds of hours of study.

That is it for now.  Today, I am just reviewing solutions.

The Importance of Meta Learning

I tend to use a variety of meta-learning techniques.  The first one is simply to monitor my daily work and progress.  I have notebooks from 30 years ago filled with my daily juggling notes, notebooks from 20 years ago full of daily banjo progress, and notebooks going back 10 years full of mathematical success and failure.  Other notebooks on my shelf document medical progress.  If I look, I could find the note from 1988 when I first was strong enough to drive a stick shift, a year after my 1987 automobile accident.

Here is a photo of what some of my notebooks look like at this very moment:


If you are curious, here is a random page from a random notebook:

The page reads:

December 15, 2003

New Things I’ve done in the last 5 days

  1. Flown in an airplane
  2. Seen the Pacific Ocean
  3. Been in California
  4. Seen the Bush Man
  5. Had an In-Out Burger
  6. Rode on a cable car
  7. Been in San Francisco
  8. Been in Hyde Park
  9. Been in the Redwood forests
  10. Had an Art Opening
  11. Ate Sushi
  12. Saw rice paddies
  13. Been in a telecommunications switching facility
  14. Saw Alcatraz
  15. Crossed the Golden Gate Bridge
  16. Flown over Salt Lake City

When working on a computer, there are other simple ways to document ones progress.  Here is a picture of the current graph of my progress on the 153 SOA sample problems:

The graph goes back about 70 days, and simply shows how many of the problems I solved each day (about 15, on average).    Those problems are only part of my daily studying.

By the way, 31 days left!!

Sorry, More Technical Stuff

Currently, I am coming to grips with the law of total variance.

In words, the variance of X equals the variance of the expected value of X, given Y, plus the expected value of the variance of X, given Y.

In symbols, Var(X) = Var(E(X|Y)) + E(Var(X|Y).

By reading the verbal definition, one can see that the logic is convoluted. Given two probability distributions, it can be tricky to see how to apply the law. Once the law is applied, there are additional tricky steps of logic involving the independence of variables.

From the SOA/CAS sample problems:

A motorist makes 3 driving errors, each independently resulting in an accident with probability 0.25.  Each accident results in a loss that is exponentially distributed with mean 0.80.  Losses are mutually independent and independent of the number of accidents.  The motorists insurer reimburses 70% of each loss.  Find the variance of the total unreimbursed loss.

The above item illustrates the technical problem that I have been having when using Spaced Repetition Software to schedule repetitions of complex material.

When I encounter a difficult item, I spend time exploring the given solution, and alternate solutions. Eventually, I move on to another item. Most likely, I am not entirely comfortable with the material, and I would like to see the same material every day for a while, to approach it with different solutions. The way that the defaults on SRS software are set up, as soon as you start rating an item anything other than the most difficult setting, the item starts getting pushed off way into the future. After a week or two weeks, I have entirely forgotten many of the finer details of the item, and it is almost as if I am starting from scratch.  For difficult material, it is beneficial to see the same items every day, or every 2nd or 3rd day.

The solution to this problem is to reset the forgetting index. In Anki, I have now set my forgetting index to 3%. This task is done by downloading the shared “Forgetting Index” plugin. In the “File” menu, select “Download Shared Plugin”, and find the forgetting index plugin.

The result is that I can now look at problems on a nearly daily basis before they start whizzing into the future. Each time I look at the problem with fresh eyes, I observe new things.

In the last week, I finally have my Spaced Repetition Software working to its utmost. I use it to schedule repetitions of difficult exam problems, and of memorization items. These are two fundamentally different tasks, so it is important to set up Anki (the software that I am now using), in two different ways.  After spending time every day for a week with the above “unreimbursed loss” problem, I look at it, and think “piece of cake.”  Now, when I encounter other law of total variance situations, I have several good comparison problems stashed away in my head.

Progress at Last

My current mantras, buzzwords, and catch-phrases:

  • Slow down, and work accurately.

  • If not now, when?

  • Just one more.

I have been here before.  My mind is finally in the right place to work many hours of mathematics each day. Each of theses three phrases have been exactly what I needed to keep myself on the right track. My current phrase is “If not now, when?” I use this phrase to realize that if I do not fully comprehend any little algebraic trick, or twist of logic, now is the only time to wrestle with it. That might involve spending a half hour, or 2 hours, with a single problem.

Wish me luck. 63 days until test time.

Tons of Problems

68 more days until SOA/CAS Exam P/1.  Although I got up late today, I still managed to work tons of problems.  My goal until test time is to do at least 30 problems each day.

I have quickly realized that using spaced repetition for difficult problems is an entirely different process from using it for simple memorization items.  If I am having any trouble at all in remembering the flow of logic of the solution, I need to repeat the problem daily, or even twice daily, until I am really sure that I understand every little twist.  Then, I start rating the item so that it comes up on a spaced repetition schedule.  It is the old truism of SRS:  you can’t learn it until you understand it:

  1. Do not learn if you do not understandTrying to learn things you do not understand may seem like an utmost nonsense. Still, an amazing proportion of students commit the offence of learning without comprehension. Very often they have no other choice! The quality of many textbooks or lecture scripts is deplorable while examination deadlines are unmovable.

    If you are not a speaker of German, it is still possible to learn a history textbook in German. The book can be crammed word for word. However, the time needed for such “blind learning” is astronomical. Even more important: The value of such knowledge is negligible. If you cram a German book on history, you will still know nothing of history.

    The German history book example is an extreme. However, the materials you learn may often seem well structured and you may tend to blame yourself for lack of comprehension. Soon you may pollute your learning process with a great deal of useless material that treacherously makes you believe “it will be useful some day”.  

  2. Learn before you memorizeBefore you proceed with memorizing individual facts and rules, you need to build an overall picture of the learned knowledge. Only when individual pieces fit to build a single coherent structure, will you be able to dramatically reduce the learning time. This is closely related to the problem comprehension mentioned in Rule 1: Do not learn if you do not understand. A single separated piece of your picture is like a single German word in the textbook of history.

Taken from the SuperMemo website.

Using SRS for studying difficult problems violates several of the other principles of SRS, but it still a simple way to schedule the problems, and to monitor progress.

More tomorrow 🙂

Study Time

69 days until Exam 1/P.  How well prepared that I feel depends upon how difficult the material is that I am studying.

Right now, I am studying some of the finer points of moment generating functions.  I have been spending 2 to 3 hours each day on problem solving, as well.  I need to increase my hours per day, as well as increasing the effectiveness of those hours.

My main way of increasing efficiency at studying is to spend regular time on creative projects.  For Exam 1/P, my creative project is my memorization cards for Anki.  Currently, have 516 cards.  I still need to add to a few areas, fill in some other areas, and add some simple numerical examples for some others.  At this point in preparing for the test, adding study cards is a bit of a sideline project.  But, I find that the creative project gets my concentration back where it should be.  Also, if I am struggling with the solution to a problem, I can dismantle the problem into its component parts.  I would still like to write one big all-inclusive “cheat sheet” for the test as well.

Until test time, I will making one short post here each day, plus adding notes on what material I have covered.  Wish me luck! 🙂

76 Days Until Exam P/1 !!!

Only 76 days left to study.

The next evolution in my study strategy is “accuracy”. At this point, I have developed a good conceptual grasp of all of the material.  I have familiarity with all of the likely problem types.  I can quickly recall hundreds of specific formulas and solution steps.  But, Exam P also tests accurate work.  Every double integration and long numerical calculation involves a risk of errors.

So, I slow down, and work accurately.