R help

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No solution exists, because the mean of a sum of n random variables 
each with mean mu is n*mu, which is different from mu if n > 1.

	  Beyond this, it is not clear to me what you want, but the following 
might help, if my understanding of your problem is close to correct:

y <- rnorm(1)
n <- 3
x <- rnorm(n)/sqrt(3)
x <- y*x/sum(x)
x; sum(x); y

hth.  spencer graves
 Hello,
 I have the normal random variables y(t)~N(mu, sigma.sq) and want to decompose them into n normal variables:

 y(t) = x(t,1) + ? + x(t,n) 

x(t,i)~N(mu, sigma.sq/n) 

 The problem is not as simple as can appear. All my experiments didn?t give me anything so far. Are there any tools to do this?

Thanks

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Shutnik <shutnik_xx at yahoo.co.uk> writes:
 Hello,
 I have the normal random variables y(t)~N(mu, sigma.sq) and want to decompose them into n normal variables:

 y(t) = x(t,1) + 
+ x(t,n)
x(t,i)~N(mu, sigma.sq/n) 

 The problem is not as simple as can appear. All my experiments didn?t give me anything so far. Are there any tools to do this?

This should work, provided I understand the problem correctly:

x <- rnorm(n,sd=sqrt(sigma.sq/n))
x <- x - mean(x) + y/n
O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
On Tue, 29 Apr 2003 20:54:25 +0100 (BST), you wrote in message
<20030429195425.18439.qmail at web10904.mail.yahoo.com>:
Hello,
I have the normal random variables y(t)~N(mu, sigma.sq) and want to decompose them into n normal variables:

y(t) = x(t,1) + 
+ x(t,n)
x(t,i)~N(mu, sigma.sq/n) 

The problem is not as simple as can appear. All my experiments didn?t give me anything so far. Are there any tools to do this?
Work out the joint distribution of the x's conditional on y, then
sample from that.  This sort of calculation appears in lots of places,
e.g. Searle (1971), Linear Models, p. 47.

Duncan Murdoch