Brian Jackson edited Whether_or_not_we_detect__.tex  almost 9 years ago

Commit id: 519e813b2f30c768e954a71ba9ded30f297d2429

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Combining the recovery bias and distortion expression gives a probability density for a devil with a given $P_{\rm act}$ to be observed with a pressure between $P_{\rm obs}$ and $P_{\rm obs} + dP_{\rm obs}$:   \begin{equation}  f\ \dfrac{dp}{dP_{\rm obs}} = \left( \dfrac{P_{\rm min}}{P_{\rm max} - P_{\rm min}} \right) P_{\rm act}\ P_{\rm obs}^{-2}.  \label{eqn:Pobs-Pact_prob_density} \label{eqn:probability-density_Pobs-Pact}  \end{equation}Figure \ref{fig:probabilty-density_Pobs-Pact} illustrates this density.