[R] How to set up a function for "Central Limit Theorem"

G. Jay Kerns gkerns at ysu.edu
Tue Mar 24 02:44:00 CET 2009


Dear Ivan,

On 3/23/09, pfc_ivan <pfc_ivan at hotmail.com> wrote:
>
> Hello guys, I am stuck here:
>
> How do I make 1000 samples of n = 10 observations from an Exponential
> distribution and then compute the mean for all those 1000 samples?
>

The R Commander will do this.  See the menus Distributions ->
Continuous -> Exponential -> Sample...

If you were wanting to normalize the row sums (or investigate the
sampling distribution of some other statistic, for that matter) then
check out the Sampling Distributions... menu in RcmdrPlugin.IPSUR.

Good luck,
Jay



> Basically I need to prove the Central Limit theorem, which states:
>
> http://www.nabble.com/file/p22664113/d175f06cbf200bd52a2c27a2e56dc594.png
>
> Where the Sn is sum of random variables, n we have from the question, mu is
> mean and (sigma)^2 is variance.
>
> I am having trouble setting up the function to do this.




***************************************************
G. Jay Kerns, Ph.D.
Associate Professor
Department of Mathematics & Statistics
Youngstown State University
Youngstown, OH 44555-0002 USA
Office: 1035 Cushwa Hall
Phone: (330) 941-3310 Office (voice mail)
-3302 Department
-3170 FAX
E-mail: gkerns at ysu.edu
http://www.cc.ysu.edu/~gjkerns/




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