this is for holding javascript data
S More edited untitled.tex
over 8 years ago
Commit id: b5e07395bc5afc6c5522935dfde5f950355f3edb
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\textit{Oh, an empty article!} \section{Introduction}
You can get started by \textbf{double clicking} this text block and begin editing. You can also click Consider the
\textbf{Text} button below to add new block elements. Or you can \textbf{drag following integral:
\begin{equation}
F = \int dx dy f P(f, \sigma)
\end{equation}
where f is the number of photon counts in a pixel $(x, y)$ and $P(f, \sigma)$ is a Gaussian distribution centered at zero and
drop an image} right onto with dispersion $\sigma$.
Assuming ergodicity, we can reduce this
text. Happy writing! integral to
\begin{equation}
F = \int_{-\infty}^{\infty} df f P(f, \sigma) = 0
\end{equation}
Instead if we decided to do,
\begin{equation}
F = \int dx dy |f| P(f, \sigma)
\end{equation}
Then we would end up with
\begin{eqnarray}
F &=& 2 \int_{0}^{\infty} df f P(f, \sigma) \\
&=& 2 \int_{0}^{\infty} df f \frac{1}{\sqrt(2*\pi)\sigma}\exp\left(-\frac{f^2}{2\sigma^2} \right) \\
&=& 2 \int_{0}^{\infty} \frac{\sigma dt}{\sqrt{2*\pi}}\exp(-t) \\
&=& \sqrt{\frac{2}{\pi}} \sigma
\end{eqnarray}