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     \title{ STAT:5400 Midterm 1, 2016} 
     \author{$<$Your Name$>$}
     \date{$<$date when you took exam$>$}
     \maketitle

\section{ \LaTeX\ } \label{sec:latex}

\begin{table}[h]
\label{mytab}
\begin{center}
\begin{tabular}{cc}
\hline
Name & PDF \\
\hline
Gamma & $p(y|\alpha, \beta) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} y ^ {\alpha - 1} exp( - \beta y)$ \\
\hline
\end{tabular}
\caption{A univariate continuous density}
\end{center}
\end{table}

Table \ref{mytab} is an excerpt from \citet{Cowl13}.

\section{R}

\begin{enumerate}
  \item  Read the data from the {\tt data.txt} file in the
Datasets section of the course web page into a dataframe in R.  
You may either save the file to disk and read it from there or read
it directly from the web site.  Then calculate
summary statistics of each column and  produce the scatterplot.  Both
outputs are shown below.

<<fig = TRUE, echo = TRUE>>=
myobj <- 
      read.table("http://homepage.divms.uiowa.edu/~kcowles/Datasets/data.txt", 
      header = TRUE)
summary(myobj)
plot( myobj, log = "y")
@
 
 \item The volume of a rectangular solid with length $l$, width $w$, and
height $h$ is $lwh$.  
\begin{enumerate}
      \item Write an R function to calculate the volume of a rectangular
solid.  It should accept a single argument -- a vector of length 3 containing
the length, width, and height.  Include the R code that defines your
function.

<<>>=
volume <- function(v)
{
  if(!(is.numeric(v) && is.vector(v) && length(v) ==3))
      {
         print("Invalid input. \n")
      }
  else
      {
        return( prod(v))
      }
}
@ 

\item Create a matrix in R with the following entries:
   \begin{verbatim}
        16.5  12.8  4.2
         3.1   2.7  8.5
   \end{verbatim}

 Consider the first column as lengths, the second column as widths, and the
third column as heights.  Write efficient R code to compute the volumes of
rectangular solids with dimensions in each row of the matrix.

<<>>=
  m <- matrix( c(16.5, 12.8, 4.2, 3.1, 2.7, 8.5), nrow = 2, byrow = TRUE)
  apply(m, 1, volume)

@


\end{enumerate}




\end{enumerate}

\bibliographystyle{apalike}
\bibliography{mid1}


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