User talk:Uncoolbob

deltazBar = a(u-zBar)+epsilon

$$\Delta \overline{z} = a(u - \overline{z}) + \epsilon$$

Deltazbar = covariance term + transmission term = Cov(w / wbar,z) + E((w  / wbar) Deltaz)

$$ \begin{array}{ll} \Delta \overline{z} & = \text{covariance term} + \text{transmission term}\\ & = \mathrm{cov}(w/\overline{w},z) + \mathrm{E}( (w/\overline{w}) \Delta z) \end{array} $$

Just Delta zBar and Delta z wBar

$$\Delta \overline{z}$$

$$\displaystyle \Delta z$$

$$\displaystyle \overline{w}$$ $$\displaystyle \overline{z}$$ $$\displaystyle w$$ $$\displaystyle z$$

zbar_O - zbar_P

$$\displaystyle z_O$$ $$\displaystyle z_P$$ $$\overline{z}_O -\overline{z}_P$$

beta(w,z) $$\displaystyle\beta(w,z)$$ $$\displaystyle\beta(w,\mathsf{CL})$$ $$\displaystyle\beta(w,\mathsf{R})$$

Mbar_t = u +(Mbar_0 – u) e-at

$$\overline{M}_t = u + (\overline{M}_0 - u) e^{-at}$$ $$\overline{M}_0$$ $$\overline{M}_t$$ $$\displaystyle a$$

$$\overline{z}_0$$

zbar_t = u + (zbar_0 – u)e^-at

$$\overline{z}_t = u + (\overline{z}_0 - u)e^{-at}$$