\[ \Pr(X \le c) = \int^c_{-\infty} f(x) \> dx \]
-\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: