Table 1.

Molecular distribution moments

Moment	Value
〈K〉	$\frac{a\theta }{\kappa }$
μN	〈K〉/β
μM	〈K〉/γ
${\sigma }_N^2-{\mu }_N$	$\frac{{\mu }_N\theta }{\kappa +\beta }$
${\sigma }_M^2-{\mu }_M$	$\frac{{\mu }_M\theta }{\kappa +\gamma }\cdot \frac{\beta }{\kappa +\beta }\cdot \frac{\kappa +\beta +\gamma }{\beta +\gamma }$
Cov(XN, K)	$\frac{⟨K⟩\theta }{\kappa +\beta }$
Cov(XM, K)	$\frac{⟨K⟩\theta }{\kappa +\gamma }\cdot \frac{\beta }{\kappa +\beta }$
Cov(XN, XM)	$\frac{⟨K⟩\theta }{\left(\kappa +\beta \right)\left(\kappa +\gamma \right)}\cdot \frac{\kappa +\beta +\gamma }{\beta +\gamma }$
RN(τ)	${\mathrm{e}}^{-\beta \tau }+\frac{\mathrm{Cov}\left(X_N,K\right)}{{\sigma }_N^2}\frac{\left[{\mathrm{e}}^{-\kappa \tau }-{\mathrm{e}}^{-\beta \tau }\right]}{\beta -\kappa }$
RM(τ)	${\mathrm{e}}^{-\gamma \tau }+\beta \frac{\mathrm{Cov}\left(X_N,X_M\right)}{{\sigma }_M^2}\frac{\left[{\mathrm{e}}^{-\beta \tau }-{\mathrm{e}}^{-\gamma \tau }\right]}{\gamma -\beta }+\beta \frac{\mathrm{Cov}\left(X_M,K\right)}{{\sigma }_M^2}$
	$\times \left[\frac{{\mathrm{e}}^{-\beta \tau }}{\left(\beta -\gamma \right)\left(\beta -\kappa \right)}+\frac{{\mathrm{e}}^{-\gamma \tau }}{\left(\gamma -\beta \right)\left(\gamma -\kappa \right)}+\frac{{\mathrm{e}}^{-\kappa \tau }}{\left(\kappa -\beta \right)\left(\kappa -\gamma \right)}\right]$