Actuarial Outpost January 2014 Exam Thread
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#1
12-02-2013, 04:34 AM
 hluu Member Join Date: Mar 2013 Posts: 66

Did not see a new thread, so I figured to start one for discussion and support.

We are about 1 to 2 months away from the Jan sitting. How is every one doing at it?

I've started using Adapt last month, and I'm slowly but surely moving up; Currently at 5.89 earned level. I've been testing with exam conditions on every one (without adjusting difficulty, no breaks or cheating), but I'm still not feeling confident yet. Questions are starting to repeat so I can't deny that these contributed to the inflation. I"m not manually adjusting my exam yet just so I can make sure I can work the repeated questions with ease. I'm hoping If I can understand all the adapt problems + the SOA problems, It'll put me in a great spot.
#2
12-02-2013, 09:01 AM
 amesk3 CAS Join Date: May 2013 Posts: 17

I've been using TIA to learn the material with just 3 more hours of lectures to go. My ADAPT subscription started just last night, so I will be taking my first PE soon (I think around end of this week when I finish TIA) to see what I need to review. I've done the end of section questions and SOA 153 throughout, so I'm hoping to see at least a mediocre score for ADAPT. The continuous section was much easier for me strangely enough, and helped me reinforce what I learned in the discrete section.
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#3
12-02-2013, 10:10 PM
 Outsanity Member CAS Join Date: Jul 2012 College: 1st year Posts: 195

Sitting exam January 10, 2014
Bad side, I still have 4 lessons on TIA left.
Good side, I can dedicate an average of 5+ hours/day of study time from now to Jan 10th. Can do 10 hours if I'm not afraid of brainfreeze. Probably going to bump to 6 hours for 2+ practice exam a day for last two weeks to exam.

Last edited by Outsanity; 12-02-2013 at 10:14 PM..
#4
12-03-2013, 11:30 PM
 Sega Member SOA Join Date: Dec 2012 College: City College of San Francisco, In Progress Posts: 31

January 10th is the magic day!
#5
12-08-2013, 05:12 PM
 *LikE-.-oMg* Member SOA Join Date: Feb 2013 Posts: 30

soooooo near and i have so much to do. sigh
#6
12-09-2013, 01:51 PM
 mpbaker22 Member Join Date: Nov 2013 College: University of Illinois alumnus Posts: 78

I'm starting to feel confident. I just posted another thread (oops)! I did the Marcel Finan book. I took a practice exam prior to the deadline date and only got a 15. On the other hand, I hadn't covered MGF, Central Limit, etc.

I still have to memorize all the formulas. I will also only have 3-4 hours max on weekdays and usually 5-7 hours Friday night and again Saturday morning.
#7
12-09-2013, 05:47 PM
 rebelarc Member CAS SOA Join Date: Dec 2013 College: Aspiring Excel Monkey Posts: 74

January 10th here we go!
#8
12-09-2013, 06:05 PM
 Outsanity Member CAS Join Date: Jul 2012 College: 1st year Posts: 195

I really don't like Moments of Multivariate Distribution. Grrr. Ugh, it'd be so much easier if I can actually understand what a moment generating formula is... Yes, I've got the format and formulas memorized, but what is it?
#9
12-10-2013, 11:14 AM
 Phileas Fogg Member SOA Join Date: Dec 2012 Posts: 1,459

Think of it as Alice (of Wonderland fame) looking at a probability density function through a magical "looking glass". It is a "distortion", if you will. This distortion, however, has some very nice mathematical properties and if you can learn to recognize a distorted "image" of a pdf, then you will be able to learn how to manipulate these distortions to determine the pdf of the result of the manipulations.
__________________
Jerry Landers: How can you permit all the suffering that goes on the world?
God: Ah, how can I permit the suffering?
Jerry Landers: Yes!
God: I don't permit the suffering. You do. Free will. All the choices are yours.
Jerry Landers: Choices? What choices?
God: You can love each other, cherish and nurture each other or you can kill each other...

#10
12-10-2013, 11:32 AM
 Phileas Fogg Member SOA Join Date: Dec 2012 Posts: 1,459

For example:

Dice.

We all know that if you roll two ordinary dice, the probability density of the sum is (oh, craps, I'm not going to include it here.)

Anyways, if you look at the mgf you can actually "factor" these dice:

$MGF(d_1) = \frac{1}{6}$e^t + e^{2t} +e^{3t} +e^{4t} +e^{5t} +e^{6t}$ = \frac{1}{6}$e^t + e^{2t}$*$1 + e^{2t} + e^{4t}$$

for the first die, and for the second die we factor it differently as

$MGF(d_2) = \frac{1}{6}$e^t + e^{2t} +e^{3t} +e^{4t} +e^{5t} +e^{6t}$ = \frac{1}{6}$e^t + e^{4t}$*$1 + e^{t} + e^{2t}$$

Now let's do a little square dance, swap factors do-si-do and promenade left to get a new pair of dice:

$MGF(d_3) = \frac{1}{6}$e^t + e^{2t}$*$1 + e^{t} + e^{2t}$= \frac{1}{6}$e^t + e^{2t} +e^{2t} +e^{3t} +e^{3t} +e^{4t}$$

for the third die, and for the fourth die we factor it differently as

$MGF(d_2) = \frac{1}{6}$e^t + e^{4t}$*$1 + e^{2t} + e^{4t}$ = \frac{1}{6}$e^t + e^{3t} +e^{4t} +e^{5t} +e^{6t} +e^{8t}$$

Now, it should be fairly obvious that "Die 3" is actually the MGF of a die with sides {1, 2, 2, 3, 3, 4} and "Die 4" is actually the MGF of a die with sides {1, 3, 4, 5, 6, 8}.

If you calculate the pdf of the sum of Die 3 and Die 4, you get exactly the same pdf of the original pair of identical dice with sides {1, 2, 3, 4, 5, 6}.

Cool, huh?

Actually, this factorization makes sense.

One way to "factor" a 6-sided die is to consider first, will the sides be "low" {1, 2, 3} or "high" {4, 5, 6}. Then we choose "left, center, or right".

So the "low vs. high" factor is basically, "do we start with a base of 1 or 4" which means a factor of $\frac{1}{2}$e^t + e^{4t}$$. Then the "left, center, or right" factor is $\frac{1}{3}$1 + e^t + e^{2t}$$, depending on whether we add 0, 1, or 2 to our base.

Alternately, we can divide the set as "even vs. odd" and "low, middle, or high"; so we start with the parity indicator (odd or even - 1 or 2) which means a factor of $\frac{1}{2}$e^t + e^{2t}$$. Then the "low, medium, or high" factor is $\frac{1}{3}$1 + e^{2t} + e^{42t}$$, depending on whether we add 0, 2, or 4 to our base.

Die 3 and Die 4 are then constructed by swapping partners, so that with Die 3 we start with 1 or 2 and then add 0, 1, or 2 to that, while with Die 4 we start with 1 or 4 and then add 0, 2, or 4 to that.

Incidentally, there is also a nice proof that there is no such thing as a true "half of a coin flip" - the square root of $\frac{1}{2}$1 + e^t$$ cannot be expressed as a polynomial (finite or otherwise) which does not include negative coefficients.

Of course, those are probability mass functions. If someone can come up with an elegant intuition like this about CONTINUOUS probability distribution functions, my hat is off to them.
__________________
Jerry Landers: How can you permit all the suffering that goes on the world?
God: Ah, how can I permit the suffering?
Jerry Landers: Yes!
God: I don't permit the suffering. You do. Free will. All the choices are yours.
Jerry Landers: Choices? What choices?
God: You can love each other, cherish and nurture each other or you can kill each other...

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