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\newcommand{\sol}[1]{\par\noindent{\bf Solution:} #1}
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\newcommand{\PP}{\mathbb{P}}

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\lhead{{\sc HW:} \hwnum}
\rhead{{\sc Page:} \thepage \,of \pageref{LastPage}}
\chead{{\sc Course:} M358K -- Applied Statistics}

\cfoot{{\sc Instructor:} Milica \v Cudina}
\lfoot{}


\begin{document}

{\bf \Large Name: 
}

\medskip

\hrule

\medskip


\begin{center}
{{\sc The University of Texas at Austin}}
\end{center}
\vspace{1ex}

\begin{center}
{\Large Homework Assignment \# \hwnum}

\medskip

\underline{\large Prerequisite material.}
\end{center}

\setcounter{section}{\hwnum}

\medskip
 

\bigskip

\paragraph{\bf Problem 4.20}

\begin{itemize}
\item[\bf a.] $\PP[A^C] = $ 
\medskip
\item[\bf b.] $\PP[\text{all are the same}] = $ 
\medskip
\item[\bf c.] $\PP[\text{at least one H and at least one T}] = $ 
\medskip
\item[\bf d.] 
Answer: 
\\
Explanation:
\\
\item[\bf e.]
Answer: 
\\
Explanation:
\\
\end{itemize}

\bigskip

\hrule

\bigskip

\paragraph{\bf Problem 4.32}

\begin{itemize}
\item[\bf a.] $\PP[\text{French}] = $ 
\medskip
\item[\bf b.] $\PP[\text{not English}] = $ 
\medskip
\end{itemize}

\bigskip

\hrule

\bigskip

\paragraph{\bf Problem 4.42}

\begin{itemize}
\item[\bf a.] 
\item[\bf b.]
\medskip
\end{itemize}

\bigskip

\hrule

\bigskip

\paragraph{\bf Problem 4.64}

\begin{itemize}
\item[\bf a.] Use the graph of the density to substantiate your
  verification!

\includegraphics[scale=0.5]{m358k-4-64.pdf}

\medskip

\item[\bf b.] $\PP[Y<1]=$
\medskip
\item[\bf c.] $\PP[Y>0.6]=$
\medskip
\end{itemize}

\bigskip

\hrule

\bigskip

\paragraph{\bf Problem 4.104}

\begin{itemize}
\item[\bf a.] $\PP[A \cap B] = $

\medskip

\item[\bf b.] Draw your Venn diagram here:
\framebox(200,100){}
 
\medskip

\item[\bf c.] $\PP[B \setminus A] = $ 
\medskip
\end{itemize}

\bigskip

\hrule

\bigskip

\paragraph{\bf Problem 4.110}

\begin{itemize}
\item[\bf a.] 

\framebox(400,100){}

\medskip

\item[\bf b.] 

\framebox(400,100){}
 
\medskip

\item[\bf c.] 
\framebox(400,100){}
 
\medskip
\end{itemize}

\bigskip

\hrule

\bigskip

\paragraph{\bf Problem 4.110}

\begin{equation}%\label{}
    \nonumber 
    \begin{split}
      \PP[A \cup B] = 
    \end{split}
\end{equation}

\newpage

\paragraph{\bf Problem 4.126}

\begin{itemize}
\item[\bf a.] 
Write the probabilities in the following table:

\medskip

\begin{tabular}{l|c|c|c|c}
& \quad BSc \quad & \quad MSc \quad & Professional & \quad PhD \quad \\
\hline
Female & & & & \\
\hline
Male & & & & \\
\end{tabular}

\bigskip

\item[\bf b.] $\PP[Female]=$
\medskip
\item[\bf c.] $\PP[Female \, |\, Professional]=$
\medskip
\item[\bf d.] 
Answer:\\

\noindent Explanation:

\framebox(400,100)[l]{
}

\end{itemize}

\bigskip

\hrule

\bigskip

\paragraph{\bf Problem 4.138}

\begin{itemize}
\item[\bf a.] Mean:\\
\noindent Standard deviation: \\
\medskip
\item[\bf b.]

\medskip
\begin{tabular}{l|c|c|c}
Value of $X$ & \quad 2 \quad & \quad 3 \quad & \quad 4 \quad \\
\hline
Probability & & & \\
\end{tabular}
\medskip
\end{itemize}
\end{document}

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