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  \usetheme{Warsaw}
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\usepackage[english]{babel}
\usepackage[latin1]{inputenc}
\usepackage{times}
\usepackage[T1]{fontenc}
\usepackage{pstricks}
\usepackage{multicol}
\usepackage{pst-all}


\begin{document}

\title{Episode 10\\ Repetitive throws of a fair die}
\subtitle{European section, season 01}
\date{}

\begin{frame}
  \titlepage
\end{frame}


\begin{frame}{Step 1}

\Large

\begin{itemize}
\item Throw the die 10 times and write down the results in a clever way.
\item Build a frequency table to show your results, with both absolute and relative frequencies.
\item Draw a relative frequency polygon in {\gray grey}, with unit 2 cm on the $x$-axis and 10 cm on the $y$-axis.
\end{itemize}


\end{frame}

\begin{frame}{Step 2}

\Large

\begin{itemize}
\item Throw the die 100 times and write down the results in a clever way.
\item Build a frequency table to show your results, with both absolute and relative frequencies.
\item Draw a new relative frequency polygon in black on the same graph as the first one.
\end{itemize}


\end{frame}

\begin{frame}{Step 3}

\Large

\begin{itemize}
\item Gather the 400 or 500 results in your group in a new frequency table.
\item Draw a new relative frequency polygon in {\blue blue} on the same graph as the first ones.
\end{itemize}


\end{frame}

\begin{frame}{Step 4}

\Large

\begin{itemize}
\item Gather the 1800 or 2000 results in the class in a new frequency table.\\
\bigskip

\begin{tabular}{c|c|c|c|c|c|c}
Face & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
Frequency & \rule{0.7cm}{0pt} & \rule{0.7cm}{0pt} & \rule{0.7cm}{0pt} & \rule{0.7cm}{0pt} & \rule{0.7cm}{0pt} & \rule{0.7cm}{0pt} \\
\end{tabular}

\bigskip

\item Draw a new relative frequency polygon in {\green green} on the same graph as the first ones.
\end{itemize}


\end{frame}

\begin{frame}{Step 5}

\Large

\begin{itemize}
\item Below are the results for a sample of 10 000 throws. Compute the relative frequencies.
\begin{center}\normalsize
\begin{tabular}{c|c|c|c|c|c|c}
Face & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
Frequency & 1752 & 1655 & 1664 & 1639 & 1674 & 1616 \\
\end{tabular}
\end{center}
\item Draw a new relative frequency polygon in {\magenta magenta} on the same graph as the first ones.
\end{itemize}

\end{frame}

\begin{frame}{Step 6}

\Large

\begin{itemize}
\item Below are the results for a sample of 50 000 throws. Compute the relative frequencies.
\begin{center}\normalsize
\begin{tabular}{c|c|c|c|c|c|c}
Face & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
Frequency & 8462 & 8220 & 8215 & 8271 & 8419 & 8413 \\
\end{tabular}
\end{center}
\item Draw a new relative frequency polygon in {\red red} on the same graph as the first ones.
\end{itemize}

\end{frame}

\begin{frame}{A possible set of graphs}

\begin{center}
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\psline[linecolor=black](0,0)(1,0.18)(2,0.18)(3,0.15)(4,0.18)(5,0.14)(6,0.17)(7,0)\pause
\psline[linecolor=blue](0,0)(1,0.192)(2,0.178)(3,0.168)(4,0.182)(5,0.152)(6,0.128)(7,0)\pause
\psline[linecolor=green](0,0)(1,0.1855)(2,0.1670)(3,0.1615)(4,0.1755)(5,0.1625)(6,0.1480)(7,0)\pause
\psline[linecolor=magenta](0,0)(1,0.1752)(2,0.1655)(3,0.1664)(4,0.1639)(5,0.1674)(6,0.1616)(7,0)\pause
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\psline[linewidth=2pt,linecolor=cyan](0,0)(1,0.1667)(6,0.1667)(7,0)
\end{pspicture}

\end{center}

\end{frame}



\end{document}
