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Brian Jackson edited subsection_The_Pressure_Depth_Recovery__.tex
almost 9 years ago
Commit id: 186eb10cd41f7875c4d9497515e481a0c0ef43e9
deletions | additions
diff --git a/subsection_The_Pressure_Depth_Recovery__.tex b/subsection_The_Pressure_Depth_Recovery__.tex
index f7ea3e9..ba652ef 100644
--- a/subsection_The_Pressure_Depth_Recovery__.tex
+++ b/subsection_The_Pressure_Depth_Recovery__.tex
...
\begin{equation}
f \equiv A(P_{\rm act})/A(P_{\rm max}) = \left( \dfrac{\Gamma_{\rm act}(P_{\rm act})}{\Gamma_{\rm act}(P_{\rm max})} \right)^2 \left( \dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm max} - P_{\rm min}} \right).
\end{equation}
For now, we'll assume $\Gamma_{\rm act}$ is independent of $P_{\rm act}$, giving
$f_{\Gamma_{\rm $f_{\left( \Gamma_{\rm act} = {\rm
const.}} const.} \right)} = \left( \dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm max} - P_{\rm min}} \right)$. As expected, the probability to detect a devil with $P_{\rm act} = P_{\rm min}$ is zero. Of course, the probability for detecting a devil with $P_{\rm act} = P_{\rm max}$ is not actually unity, just the relative probability. Calculating the actual probability would require us to define the total area of the arena over which observations were made, e.g. the area of the playa where the barometer was deployed.