deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index cd959e7..5b11d16 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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This being said, this is not what we are interested in. Really, we are interested in the average mass per bin. This is easy if we are binning on mass. Simply:  \begin{equation}  \langle M \rangle = \frac{\int_{min(bin)}^{max(bin)} \frac{\int  M \frac{d \langle n \rangle}{dM} dM}{\int_{min(bin)}^{max(bin)} dM}{\int  \frac{d \langle n \rangle}{dM} dM} \end{equation}  But unfortanately, we are not binning on mass in the real universe. Instead, we are binning on some observable $\hat{\theta}$ and asking what is the probability of observing $M$. This switches some things around in the integrals, so let's take a look.