actuary

Let me introduce some wisdom of actuary exam(s) by several post after this. I have maintained a Japanese blog "The research of the actuary exam mathematics." (in Japanese "Actuary shiken suugaku no kenkyu") http://d.hatena.ne.jp/actuary_math/ Of course the blog is intended for the examinee of IAJ(the Institute of Actuaries of Japan) but the techniques written there will be served to other examinees for example SOA(Society of Actuaries),CAS(Casualty Actuary Society), etc. First, I will introduce http://d.hatena.ne.jp/actuary_math/20080705 by translating into English. The following question is a little alternation from one seen in the past exam. Question In the above picture, AB is parallel to x-axis and AC is parallel to y-axis. (X,Y) are 2 dimensional random variables which follow uniform distributions on triangle ABC. The correlation coefficient X,Y rho(X,Y) is [ ] (fill in the blank) ---------- In this question neither the position (x,y) of A the nor the length of AB or AC are not given. So some of you may begin to present the position and the length as some variances. However, we will make the perceptional change. That is "The answer is the same even if the position (x,y) of A the or the length of AB or AC. Therefore, we can let them whatever we like.｣(*) So we will let A(0,0),B(1,0),C(0,1). E(X)=E(Y) =2{\int_0^{1} xdx \int_0^{1-x}dy} (I will mean "\int_a^b" by integral from a to b as TEX usage) =2 \int_0^1 (x-x^2)dx =2(1/2 - 1/3)=1/3 E(X^2) =2 \int_0^1 x^2dx \int_0^{1-x}dy =2 \int_0^1 (x^2-x^3)dx =2(1/3 - 1/4)=1/6 V(X)=V(Y) =E(X^2)-{E(X)} ^2 =1/6-(1/3)^2=1/18 E(XY) =2 \int_0^1 xdx \int_0^{1-x} ydy = \int_0^1 x(1-x)^2 dx =\int_0^1 (x-2x^2+x^3) dx =1/2 - 2/3+ 1/4=1/12 Cov(X,Y) =E(XY)-E(X)*E(Y) =1/12 - 1/3*(1/3)=- 1/36 rho (X,Y) =Cov(X,Y)/sqrt{V(X)*V(Y)} =(-1/36)/(1/18)=-1/2 (*)The ideas can be authorized as follows. First we put the position of A is (a,b ) and the length of AB and AC are c and d respectively. Then we put X'=(X-a)/c, Y'=(Y-b )/d as rho (X,Y)=rho (X',Y') (Because the correlation coefficient does not vary by addition, subtraction, multiplication and division of constants.) In the original question A is the Original point(0,0) and the length of AB=a and AC=b were given. But according to the above thought, we can easily find that the answers with a,b are all WRONG. The idea can not be limited to the actuary examination, and to be applicable to all objective type examinations.

I believe that how few we consider the âparameter riskâ. Suppose that the probability of occurring a accident is P (0<P<1). For N polices, the probability of occurring n accidents is N_C_n * P^n * (1-P)^(N-n) (where N_C_n means the combinatorial number which is chosen n things form N things) Suppose that the p.d.f.(probability density function) of the prior distribution is g(p), f(p),the p.d.f. of the posterior distribution by Bayes' theorem will be proportional to P^n * (1-P)^(N-n) *g(p) (because N_C_n is a constant which has no relations with p) Now if the prior distribution is a uniform distribution, that is g(p)=1(0<p<1) f(p) is proportional to P^n*(1-P)^(N-n) so P follows to B(n+1,N+1)(beta distribution).

I once used "BSMTP.DLL" which can be downloaded in http://www.hi-ho.ne.jp/babaq/basp21.html The usage is in http://www.hi-ho.ne.jp/babaq/vbtips.html These are japanese site and of course I know you can not read Japanese. But I believe you can use it only if you follow English parts.

Thank you very much for your kindly advice. But it seemed to me that I can NOT see your last image you pasted.

It seems that if you download MediaPlayer Classic https://sourceforge.net/projects/guliverkli/ and Real Alternative(codec) http://finalbuilds.com/ ,you will be able to play *.rm.

I visited your site and I found that your site used a flash(.swf) file and required latest flash player. I think this may be the reason why the Turkey could not visit.

Thank you for your reply.But I am sorry that I have already known mimetex. I am worried that mimetex does not store the images, so the cgi must be called whenever the formulae will be written and it will take much time.(I plan to use more than 100 formulae a page). If I can use the texvc, the images are stored in the homepage so it will shorten the time.

It would be very grad for me to be told whether Xisto's PHP mode is safe mode or not.I would like to run latex and so on through PHP exec command.But if the PHP mode is safe mode, I will not be able to run them well.

Please be careful that "dot.tk" is NOT a free domain. This is a kind of forwarding. For examaple, http://forums.xisto.com/no_longer_exists/ is my "dot.tk" site, but the site is the forwarding of my free blog http://d.hatena.ne.jp/actuary_math/

I would like to run mediawiki with texvc on this webhosting "Xisto.com"I came to this site by searching at Google with the word "Imagemagick"Can we run mediawiki and texvc on "Xisto.com"?

I am an actuary.I am interesting in actuarial science.Let us talk about actuarial science.