s

and

s^{'}

in the same galaxy, the shared fluctuation is the only common random term. Independence and linearity of covariance therefore give

Cov (M_{s}, M_{s^{'}}) = σ_{G}^{2}, Var (M_{s}) = σ_{G}^{2} + σ_{I}^{2} \equiv σ_{tot}^{2} .

Corr (M_{s}, M_{s^{'}}) = \frac{σ _{G}^{2}}{σ _{G}^{2} + σ _{I}^{2}} .

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