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" <[EMAIL PROTECTED]>
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
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