I just did this last night for a class. It's very simplistic and could be improve, but it did the job. First I did the normal. Of course means of increasing large samples from a normal stay normal. This setup the students. Then I did means from an exponential. For n=1 you get the exponential again, and they of course expected the means with larger n's to also follow the exponential! Got 'em! Joe
#Central Limit Theorem oldpar = par(mfrow=c(2,2)) #Normal n=64 #Do it repeatedly for n=1 4, 16, 64, 100 d=numeric(1000) for (k in 1:1000){d[k]=mean(rnorm(n,mean=5,sd=16))} c(mean=mean(d),sd=sd(d)) plot(density(d),col='blue') curve(dnorm(x,mean=5,sd=16/sqrt(n)),add=T,col='red') #Exponential n=64 #1, 4, 16, 64, 100 d=numeric(1000) for (k in 1:1000){d[k]=mean(rexp(n,rate=1/4))} c(mean=mean(d),sd=sd(d)) plot(density(d),col='blue') curve(dnorm(x,mean=4,sd=4/sqrt(n)),add=T,col='red') par(oldpar) -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Paul Smith Sent: Thursday, April 21, 2005 12:07 PM To: r-help@stat.math.ethz.ch Subject: [R] Using R to illustrate the Central Limit Theorem Dear All I am totally new to R and I would like to know whether R is able and appropriate to illustrate to my students the Central Limit Theorem, using for instance 100 independent variables with uniform distribution and showing that their sum is a variable with an approximated normal distribution. Thanks in advance, Paul ______________________________________________ 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