\subsection*{Combinatorics}
-\begin{itemize} \tightlist
- \item Arrangements \({n \choose k} = \frac{n!}{(n-k)}\)
- \item \colorbox{highlight}{Combinations} \({n \choose k} = \frac{n!}{k!(n-k)!}\)
- \item Note \({n \choose k} = {n \choose k-1}\)
-\end{itemize}
+\begin{align*}
+ \text{Arrangements} && {n \choose k} & = \frac{n!}{(n-k)} \\
+ \text{Combinations} && {n \choose k} & = \frac{n!}{k!(n-k)!}
+\end{align*}
+
+Note \({n \choose k} = {n \choose k-1}\)
+
+\begin{cas}
+ Keyboard \(\rightarrow\) Advance \(\rightarrow\) \keystroke{nCr}/\keystroke{nPr} \\
+ \-\hspace{1em} \texttt{nCr(n, r)} or \texttt{nPr(n, r)}
+\end{cas}
\subsection*{Distributions}
\[ \Pr(X \le c) = \int^c_{-\infty} f(x) \> dx \]
-\begin{cas}
- Define piecewise functions: \\
- \-\hspace{1em}Math3 \(\rightarrow\)
- \begin{tikzpicture}%
- \draw rectangle (0.5,0.5);
- \node at (0.08,0.25) {\(\{\)};
- \filldraw [black] (0.15, 0.4) rectangle(0.25, 0.3);
- \draw (0.35, 0.4) rectangle(0.45, 0.3);
- \node [font=\footnotesize] at (0.3,0.3) {\verb;,;};
- \draw (0.15, 0.2) rectangle(0.25, 0.1);
- \node [font=\footnotesize] at (0.3,0.1) {\verb;,;};
- \draw (0.35, 0.2) rectangle(0.45, 0.1);
- \end{tikzpicture}
- % TODO: finish this section
-\end{cas}
-
\subsection*{Two random variables \(X, Y\)}
If \(X\) and \(Y\) are independent: