deletions | additions       diff --git a/Consider_how_the_contours_behave__.tex b/Consider_how_the_contours_behave__.tex  index 0c670d2..dafb192 100644  --- a/Consider_how_the_contours_behave__.tex  +++ b/Consider_how_the_contours_behave__.tex 
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n(P_{\rm obs}) = \left( \dfrac{P_{\rm min}}{P_{\rm max} - P_{\rm min}} \right) P_{\rm obs}^{-2} \int_{P_{\rm act} = P_{\rm obs}}^{P_{\rm max}} n(P_{\rm act}) P_{\rm act}\ dP_{\rm act}.  \label{eqn:n_Pobs_from_Pact}  \end{equation}  The integral extends between $P_{\rm obs}$ and $P_{\rm max}$ since only devils with $P_{\rm act}$ in that range can contribute. Consider, for example, a uniform distribution $n(P_{\rm act}) = k = {\rm const.}$, which give rise to $n(P_{\rm obs}) = \frac{1}{2} k\ \left( \dfrac{P_{\rm min}}{P_{\rm max} - P_{\rm min}} \right) \left[ \left( \dfrac{P_{\rm max}}{P_{\rm obs}} \right)^2 - 1\right]$. Figure \ref{fig:n-Pobs_from_uniform_n-Pact} compares the two distributions.