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\begin{document}

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\date{September 2, 2004}

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\title{Stat 312: Lecture 01\\
R Basics}

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\author{Moo K. Chung\\
mchung@stat.wisc.edu}

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\begin{enumerate}
\item {\em Data loading.} Let's illustrate basic R commands by
following example 1.5 about binge drinking in college. Data is the
percentage of binge drinkers on 140 campuses across the United
States.

\begin{verbatim}

> library(Devore6)
> data(xmp01.05)
>attach(xmp01.05)
> xmp01.05
    bingePct
1          4
2         11
3         13
.
.
.
.
138       67
139       67
140       68
\end{verbatim}

\begin{figure}
\centering
\includegraphics[width=70mm]{00-1.ps}
\caption{Histogram for binge drinker data}\label{fig:hist}
\end{figure}
\item {\em Histogram.} Let's see some basic R commands.
\begin{verbatim}
> a<-bingePct
> mean(a)
[1] 42.33571
> var(a)
[1] 205.8361
> sd(a)
[1] 14.34699
> hist(a)
\end{verbatim}
To find out more about {\tt hist} command, use\\ {\tt > help(hist)}.
It will display a new window with detailed information about {\tt
hist}.

\item Binge drinking percentage can be modeled statistically. Let $X_i$ is the binge
drinking percentage at $i$-th campus which is distributed normally
with mean $40$ and standard deviation of $14$, i.e. $X_i \sim
N(40,14^2)$. Since binge drinking percentages in different campuses
should be independent, $X_i$'s should be assumed to be independent
random variables.

\item $X_1,\cdots, X_n$ form a {\em random sample} if $X_i$ are
independent and identically distributed random variables. A {\em
statistic} is a random variable. Hence {\em sample mean} $\bar X =
\sum_{i=1}^n X_i/n$ is a statistic. It will be distributed as
$$\bar X \sim N(40/140, 14^2/140).$$



{\em Note.} Read section 5.4, 5.5 and do Ex.5.48. 5.52. 5.63.
Lecture 2-4 will be based on sections 6.1-6.2.
\end{enumerate}

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