From 2eaddbf90b80eecb7259b61b2c5ab6acf22bb6f8 Mon Sep 17 00:00:00 2001
From: Jan Benda <jan.benda@uni-tuebingen.de>
Date: Mon, 2 Dec 2019 12:10:40 +0100
Subject: [PATCH] [statistics] shortened exercise01

---
 statistics/exercises/exercises01.tex | 49 +---------------------------
 1 file changed, 1 insertion(+), 48 deletions(-)

diff --git a/statistics/exercises/exercises01.tex b/statistics/exercises/exercises01.tex
index f4fa7be..68455b3 100644
--- a/statistics/exercises/exercises01.tex
+++ b/statistics/exercises/exercises01.tex
@@ -1,4 +1,4 @@
- \documentclass[12pt,a4paper,pdftex]{exam}
+\documentclass[12pt,a4paper,pdftex]{exam}
 
 \usepackage[english]{babel}
 \usepackage{pslatex}
@@ -242,53 +242,6 @@ that are symmetric around the mean?
 \end{solution}
 
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\question \qt{Central limit theorem} 
-According to the central limit theorem the sum of independent and
-identically distributed (i.i.d.)  random variables converges towards a
-normal distribution, although the distribution of the randmon
-variables might not be normally distributed.
-
-With the following questions we want to illustrate the central limit theorem.
-\begin{parts}
-  \part Before you continue reading, try to figure out yourself what
-  the central limit theorem means and what you would need to do for
-  illustrating this theorem.
-
-  \part Draw 10000 random numbers that are uniformly distributed between 0 and 1
-  (\code{rand} function).
-
-  \part Plot their probability density (normalized histogram).
-
-  \part Draw another set of 10000 uniformly distributed random numbers
-  and add them to the first set of numbers.
-
-  \part Plot the probability density of the summed up random numbers.
-
-  \part Repeat steps (d) and (e) many times.
-
-  \part Compare in a plot the probability density of the summed up
-  numbers with the normal distribution
-  \[ p_g(x) =
-  \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}\]
-  with mean $\mu$ and standard deviation $\sigma$ of the summed up random numbers.
-
-  \part How do the mean and the standard deviation change with the
-  number of summed up data sets?
-
-  \part \extra Check the central limit theorem in the same way using
-  exponentially distributed random numbers (\code{rande} function).
-\end{parts}
-\begin{solution}
-  \lstinputlisting{centrallimit.m}
-  \includegraphics[width=0.5\textwidth]{centrallimit-hist01}
-  \includegraphics[width=0.5\textwidth]{centrallimit-hist02}
-  \includegraphics[width=0.5\textwidth]{centrallimit-hist03}
-  \includegraphics[width=0.5\textwidth]{centrallimit-hist05}
-  \includegraphics[width=0.5\textwidth]{centrallimit-samples}
-\end{solution}
-
-
 \end{questions}
 
 \end{document}
\ No newline at end of file