Course 4 Answers

[dfeucht]

The urban v rural weights were easy to calculate based on the means but I still don't think you needed that (I guess we will find out soon enough) but I think JRL is right ("There are an equal number of bus. and pleasure use" implies that business vs. pleasure is your class definition) although that isn't really an clear cut assumption and may be incorrect.

What MLE were we finding for the exponential data that had been truncated at 100. I thought it was the theta for the loss function which would have been 173 but I think I missed a shift parameter unless that again is inherent in the fact that they truncated the data.

I love the weeks after exams.... uggh

[dfeucht]

P30 Loss models

The kth raw moment is =

E(X^k)

this makes the answer E I am about 95% positive (I was 100% until half of those with answers thought D)

Again, how long will the SOA wait before posting the test and answers? The exam packet says they will be available "about November 28", but it didn't take that long last year, did it?

dfeucht, what number is that problem?




<font size=-1>[ This Message was edited by: Pita on 2001-11-06 15:33 ]</font>

[M.]

SOA only started posting answers with the May 2001 sitting, so we don't have much history to make a guess on a release date. I'm hoping they'll release the Course 4 answers as early as next week, because they waited less than a week to post the Course 5 MC answers.

<font size=-1>[ This Message was edited by: M on 2001-11-06 15:34 ]</font>

[erickson]

Here are a few more questions (and my answers). . .

1) #19 or # 20 -- first of 2-parter: calculate S(both) - S(B) using P-L estimator. Answer: .0667

2) Which of the following is false regarding Time Series: "Yule-Walker equations are sufficient."

3) There was a Poisson-gamma conj prior question. Gamma's theta was 1/500 --> K = 500 --> Z = 1500 / (1500 + 500) --> I forgot the answer

4) There was a question where you get 11(1/9)*Z + (old mean)*(1-Z). The answer here was 12.

5) YX^(1/4) = alpha*X^(1/4) + beta*x^(5/4) + e* is the answer to the non-constant variance regression question.

6) There was a question regarding MLE and a mixed exponential (one theta=100; one theta=10,000). The answer was D -- too long to write out.

7) What did everyone get for the CV of theta(hat) which is calculated via MLE? I got .45, but I don't remember how confident I was.

There was a Survival Models cohort (life table) question. I think the answer was (8/9)*(5/6) = 40/54.

9) What was the answer to the Survival Models question regarding lagged claim times/pmt? It required reversing the time scale, but I got stuck and panicked as time ran out. Had to guess. . .

10) I calculated an F-ratio to be 17.5 when comparing R vs. UR models.

11) There was also a question where you had to test whether beta(3) = 1-beta(2) or something like that. I tested model III vs. model I, but don't remember the result. I don't think this is the same question as (10) above, but it could be.

12) There was an ARMA(1,1) question, but I don't remember the details nor the answer I chose.

13) There was a question re 15 autocorrelation coefficients. Then you had to choose the true statement. I chose E, but am having second guesses: "because chi-square stat is not significant at 5% level, you can accept the null with 95% probability."

14) Another question had a uniform (0,theta) with f(theta) = 500/(theta^2). I think I picked D, but I also think it was a guess. . .

[erickson]

darn emoticons!

[C8 Guy]

I weighted them all equally. I don't if it's right but it worked out to a given answer.




The raw moment is E[X^k]=1/N*SUM(Xi^k)

The moment about the mean is:

1/N*SUM[(Xi-Xbar)^k]

[erickson]

There was also a question re coin flips: the observation was H,H,T,H and the risk types were: [p(heads);a priori] -- [.5;2/3],[.25;1/6],[.75;1/6]. I don't remember the answer, but it's a straight-forward bayesian analysis problem.

[Actuary321]

OK maybe I should have said the 'raw' question was rhetorical (sp?). My point is I hate questions where they use a word differently just to throw you off.

And some people above used some wild formula using cubes to figure it because it was grouped data and they told you that the data were assumed to be uniformly distributed over each interval.

I figured that it had to be harder than just taking a weighted average of the squares of the midpoint of each interval using the claims in each interval as the weights. But alas I couldn't remember those formuli so I just calculated it the easy way hoping that it would not differ enough to make a difference, Right.

On 2001-11-06 13:57, Bullseye wrote:
New Question: The buhlmann credibility question where you drove for business and personal in urban and rural regions...Did you need the breakout mean and variance for urban and rural or could you ignore that and use the totals provided for business and personal ? ( I hope this question makes sense ?

I'm pretty sure you need to split it into Urban and Rural. You can think of Urban and Rural as being different years of claims and then the problem is much like problems on past exams.