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October 20th, 2011, 09:52 AM   #1
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Random sample with zero sample mean

I want to draw a random sample, x_1,...,x_N from a NORMAL(0,sigma^2)-distribution. The problem is that I need the generated sample mean to be zero (i.e. mean(x_j)=(1/N)*sum(x_j)=0). To do this I guess that the independence assumption of the sample must be relaxed.

For even N:s my suggestion is to draw x_1 to x_{N/2} by a random number generator and then set x_{N/2+j}=-x_j (j=1,...,N/2). Then each x_j (j=1,...,N) is NORMAL(0,sigma^2) and mean(x_j)=0.

Is this idea proper? Are there any standard ways of dealing with my problem? How should I do for odd N?
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