On 05-Dec-05 Duncan Murdoch wrote: >> The variance of X is (or damn well should be) defined as >> >> Var(X) = E(X^2) - (E(X))^2 >> >> and this comes to (Sum(X^2) - (Sum(X)/N)^2))/(N-1). > > I don't follow this. I agree with the first line (though I prefer to > write it differently), but I don't see how it leads to the second. For > example, consider a distribution which is equally likely to be +/- 1, > and a sample from it consisting of a single 1 and a single -1. The > first formula gives 1 (which is the variance), the second gives 2. > > The second formula is unbiased because in a random sample I am just as > likely to get a 0 from the second formula, but I'm curious about what > you mean by "this comes to". > > Duncan
Sorry, you're of course right -- I was being a bit hasty and maganed to tangle this with a standard definition of the "variance" of a finite population which uses the 1/(N-1) divisor! -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 05-Dec-05 Time: 20:08:38 ------------------------------ XFMail ------------------------------ ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
