The Final Countdown

This is it. Yesterday, I paid for my exam through the Society of Actuaries. Today, I scheduled the exam, for March 19, 2012. That makes 53 days to study. If I solve 30 problems per day between now and then, that is 1500 hundred more problems. I think that I will start a little counter in my “To Do” notebook, to tally my total. (A “To Do” notebook is sort of like a smart phone, and kind of like a computer, and kind of like a personal assistant. I can’t survive more than two hours without one. Actually, a “To Do” notebook is even more like a brain, except much more functional.)

In other news, the kitchen is nearly demolished. The plumber came yesterday to rip the old sink out, so now we are left with a filthy, crater ridden floor.

The next big project is removing the fridge from the kitchen. I put aside one entire day of work for this project, and it will take at least that. First, the doors need to be unwired, unhosed, and removed. Then the fridge needs to be moved through a narrow door. Finally, the fridge needs to be redoored, rewired, and replumbed. All of that, after having already unjointed my back trying other techniques.

Wish me luck.

Job Description

FonziFonzi Dog

Duties:

  • Snuggle
  • Be nice to kitties
  • Guard house from mail carrier
  • Greet visitors at door
  • Keep lap warm
  • Play
  • Run around house very wild
  • Give kisses
  • Resist strong urges to eat cat poop

Compensation:

  • Room and Board
  • Bones
  • Personal sleepy chair next to bed
  • One very long walk per day, plus one short walk
  • Regular prunings (Jimothy back end, Helen front end)
  • Free medical care, including regular preventative checkups, plus emergency service
  • Scratches
  • Tummy Wubs
  • Occasional showers
  • Toy selection in basket, as well as life-size dog puppet (Tumbleweed) for dragging around the house.

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! 🙂