From: Dimitris Rizopoulos <dimitris.rizopoulos_at_med.kuleuven.ac.be>

Date: Tue 01 Mar 2005 - 20:01:35 EST

Dimitris Rizopoulos

Ph.D. Student

Biostatistical Centre

School of Public Health

Catholic University of Leuven

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Mar 01 20:07:08 2005

Date: Tue 01 Mar 2005 - 20:01:35 EST

a simple approach could be:

n <- seq(10, 5000, 10)

means <- numeric(length(n))

for(i in seq(along=n)){

mat <- sample(1:6, 2*n[i], TRUE); dim(mat) <- c(n[i], 2)
means[i] <- mean(ifelse(!mat[,1]%%2, mat[,1], -mat[,2]))
}

means

plot(n, means, xlab="sample size", ylab="mean")

I hope it helps.

Best,

Dimitris

Dimitris Rizopoulos

Ph.D. Student

Biostatistical Centre

School of Public Health

Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium

Tel: +32/16/336899 Fax: +32/16/337015 Web: http://www.med.kuleuven.ac.be/biostat/ http://www.student.kuleuven.ac.be/~m0390867/dimitris.htm

- Original Message ----- From: "Jacob van Wyk" <jlvw@na.rau.ac.za> To: <r-help@stat.math.ethz.ch> Sent: Tuesday, March 01, 2005 9:25 AM Subject: [R] Beginner - simple simulation

> Hallo to everybody. I am new to the list and would appreciate some

*> help
**> in a basic "first demo" of how to use R for simulating a simple
**> game; I
**> would like my students to use R and this may stimulate their
**> interest.
**>
**> The problem is simply:
**>
**> Two players (A and B) play the following game. Each player rolls a
**> die
**> (fair, 6-sided) and they write down the result: say A rolls nA and B
**> rolls nB. If nA is even, A pays B $nB: if nA is odd, B pays A $nA
**> (we
**> think of A paying B a negative amount). The amount that A pays B is
**> a
**> random variable X. Find the expectation of X.
**>
**> Theoretically it is 1/4 - B is ahead on average with 25c.
**>
**> Would anybody be prepared to help a little. I want to avoid loops
**> and
**> vectorize the computations, simulate the value of X for various
**> sample
**> sizes and preparea basic plot to show that the average value of X
**> "converges" to 1/4.
**>
**> I would start with, say,
**> sample(1:6,2,replace=T)
**> for one simulated roll of the two dice. I want to repeat this n
**> times,
**> where n is, say, 10:2000 in steps of 10. Put the results in a matrix
**> and
**> work columnwise - choosing when the first roll is even, selecting
**> the
**> corresponding value of the second roll, and computing the payoff as
**> described, etc. But I need help to put this together.
**>
**> In Matlab I would, for example, do the following to display the
**> average
**> payouts of A and B:
**>
**> c=1;
**> samplesizes=[10:10:2000];
**> for s=samplesizes
**> rolls=ceil(6*rand(s,2));
**> a_pays_b_index=find(mod(rolls(:,1),2)==0);
**> a_pays_b_value=rolls(a_pays_b_index,2);
**> b_pays_a_index=find(mod(rolls(:,1),2)==1);
**> b_pays_a_value=rolls(b_pays_a_index,1);
**> a_pays_average(c)=mean(a_pays_b_value);
**> b_pays_average(c)=mean(b_pays_a_value);
**> c=c+1;
**> end
**>
**> Then do the plotting, etc. (One could also take differences, and so
**> on.)
**>
**> I would really appreciate if anybody would be kind enough to help. I
**> thought it might be a nice example to introduce students (in
**> general,
**> perhaps - because it is a kind of interesting game) to simulation in
**> R.
**>
**> Thank you !
**> Jacob
**> (PS Any credit would be respected, i.e. my students will know who
**> helped me with this introduction.)
**>
**>
**>
**>
**> Jacob L van Wyk
**> Department of Mathematics and Statistics
**> University of Johannesburg APK
**> P O Box 524
**> Auckland Park 2006
**> South Africa
**> Tel: +27-11-489-3080
**> Fax: +27-11-489-2832
**>
**> ______________________________________________
**> R-help@stat.math.ethz.ch mailing list
**> https://stat.ethz.ch/mailman/listinfo/r-help
**> PLEASE do read the posting guide!
**> http://www.R-project.org/posting-guide.html
**>
*

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Mar 01 20:07:08 2005

*
This archive was generated by hypermail 2.1.8
: Fri 03 Mar 2006 - 03:30:38 EST
*