A correlation coefficient is computed as r=cov(X,Y)/sqrt(Var X)*sqrt(Var Y) What is the correlation coefficient of a number with itself then. I have a noise function,assuming with a known value and variance; and I perform a correlation of noise with itself what should I get as the correlation coefficient. The noise follows a chi square distribution.

A correlation coefficient is computed as $$r=Cov(X,Y)/(\sqrt{Var( X)}*\sqrt{Var (Y)})$$ What is the correlation coefficient of a number with itself then. I have a noise function,assuming with a known value and variance; and I perform a correlation of noise with itself what should I get as the correlation coefficient. The noise follows a $\chi^2$ distribution.