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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.

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No matter what distribution the variable $X$ distributed as, the correlation between $X$ and itself equals 1.

$$r=Cov(X,X)/\sqrt{Var (X)}*\sqrt{Var( X)}=Var(X)/Var (X)=1.$$

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