= Solution
Normalize both <fluorescent reporter> intensities by their respective means, correcting unequal brightness and background, and denote them $c,y$. <Extrinsic gene-expression noise> changes shared cellular conditions and moves both signals together: the scatter is a long narrow cloud around $y=c$. <Intrinsic gene-expression noise> comes from distinct random expression events in the two <genes> and broadens the cloud across that diagonal. Comparable contributions therefore give a noticeably wider, still positively correlated cloud. The two right-hand panels in the preceding original illustration show these two cases.
For matched <fluorescent reporters> with conditionally independent intrinsic fluctuations and corrected measurement noise,
$$
\eta_{\rm int}^2=\frac12\mathbb E(c-y)^2,\qquad
\eta_{\rm ext}^2=\mathbb E(cy)-1.
$$
The first quantity measures differential variation; the second measures common variation. A clone's successive observations can remain correlated in time, so they need not be independent samples. Shared activation transients should also be separated from the fluctuations of interest.<Stochastic Gene Expression in a Single Cell by Michael B. Elowitz and others>[Science 297 (2002), pp. 1183–1186: dual-reporter discrimination of intrinsic and extrinsic variation]{ref}
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