\colorbox{cas}{On CAS:} Main \(\rightarrow\) Interactive \(\rightarrow\) Distribution \(\rightarrow\) \verb;binomialPDf; \\
Input \verb;x; (no. of successes), \verb;numtrial; (no. of trials), \verb;pos; (probbability of success)
+ \subsection{Applications of binomial distributions}
+
+ \[ \Pr(X \ge a) = 1 - \Pr(X < a) \]
+
+ \subsection{Expected value of a binomial distribution}
+
+ \[ E(X \sim \operatorname{Bi}(n,p))=np \]
+
+ \subsection{Variance}
+
+ \[ \sigma^2(X) = np(1-p) \]
+
+ \subsection{Standard deviation}
+
+ \[ \sigma(X) = \sqrt{np(1-p)} \]
+
\end{document}