On 6/27/07, John Randall <[EMAIL PROTECTED]> wrote:
=\sum ((X_i-\mu)^2) -n(\bar X-\mu)^2$, since $\sum (X_i-\mu)=(\sum X_i) - n\mu = n(\bar X-\mu)$.
Ok, but these are all zero for the case where you're working with an accurate model -- where \mu and \bar X are equal. Mathematically speaking, I don't see this as a valid approach. Numerically speaking, even if they're "just close" instead of "identical", we're heading into unstable territory. Put differently: as far as I can see, I have to accept the definition of standard deviation as an axiom, if I am going to work with it at all. -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
