From: Kevin E. Thorpe <kevin.thorpe_at_utoronto.ca>

Date: Fri 13 May 2005 - 22:28:05 EST

Date: Fri 13 May 2005 - 22:28:05 EST

The variance of U[0,1] is 1/12. So the variance of the mean of uniforms
is 1/12k.

Rather than dividing by 1/12k he multiplied by 12k.

Kevin

Bliese, Paul D LTC USAMH wrote:

>Interesting thread. The graphics are great, the only thing that might be

*>worth doing for teaching purposes would be to illustrate the original
**>distribution that is being averaged 1000 times.
**>
**>Below is one option based on Bill Venables code. Note that to do this I
**>had to start with a k of 2.
**>
**>N <- 10000
**> for(k in 2:20) {
**> graphics.off()
**> par(mfrow = c(2,2), pty = "s")
**> hist(((runif(k))-0.5)*sqrt(12*k),main="Example Distribution 1")
**> hist(((runif(k))-0.5)*sqrt(12*k),main="Example Distribution 2")
**> m <- replicate(N, (mean(runif(k))-0.5)*sqrt(12*k))
**> hist(m, breaks = "FD", xlim = c(-4,4), main = k,
**> prob = TRUE, ylim = c(0,0.5), col = "lemonchiffon")
**> pu <- par("usr")[1:2]
**> x <- seq(pu[1], pu[2], len = 500)
**> lines(x, dnorm(x), col = "red")
**> qqnorm(m, ylim = c(-4,4), xlim = c(-4,4), pch = ".", col = "blue")
**> abline(0, 1, col = "red")
**> Sys.sleep(3)
**> }
**>
**>By the way, I should probably know this but what is the logic of the
**>"sqrt(12*k)" part of the example? Obviously as k increases the mean
**>will approach .5 in a uniform distribution, so runif(k)-.5 will be close
**>to zero, and sqrt(12*k) increases as k increases. Why 12, though?
**>
**>PB
**>
**>
*

-- Kevin E. Thorpe Biostatistician/Trialist, Knowledge Translation Program Assistant Professor, Department of Public Health Sciences Faculty of Medicine, University of Toronto email: kevin.thorpe@utoronto.ca Tel: 416.946.8081 Fax: 416.971.2462 ______________________________________________ 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.htmlReceived on Fri May 13 22:33:04 2005

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