<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt,pdftex]{exam}

\newcommand{\ptitle}{Fano factor test}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}

\begin{document}

\input{../instructions.tex}


%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\begin{questions}
  \question The Fano factor $F=\frac{\sigma^2}{\mu}$ relates the
  variance of a spike count $\sigma^2$ to the mean spike count
  $\mu$. It is a common measure in neural coding because a Poisson
  process---for which each spike is independent of every other---has a
  Fano factor of one.
  
  The accompanying file contains two vectors with spike counts from
  two neurons each measured in a time window of 1s.

  \begin{parts}
    \part Plot the spike counts of both neurons appropriately.
    \part Use {\em Eden, U. T., \&amp; Kramer, M. (2010). Drawing
      inferences from Fano factor calculations. Journal of
      Neuroscience Methods, 190(1), 149--152} to construct a test that
    uses the Fano factor as test statistic and tests against the Null
    hypothesis that the spike counts come from a Poisson process.
    \part Implement the test and use it on the data above.
  \end{parts}

\end{questions}



\end{document}
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