[methods] Bernoulli distributions

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+\usepackage{keystroke}
+\usepackage{listings}
+\usepackage{xcolor} % used only to show the phantomed stuff
+\definecolor{cas}{HTML}{e6f0fe}

 
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+  \colorbox{cas}{On CAS:} (soft keys) \keystroke{\(\downarrow\)} \(\rightarrow\) \keystroke{Advanced} \(\rightarrow\) \verb;nCr(n,cr);
+
+  \section{Binomial distributions}
+
+  (aka Bernoulli distributions)
+
+  \begin{align*}
+    \Pr(X=x) &= {n \choose x} p^x (1-p)^{n-x} \\
+    &= {n \choose x} p^x q^{n-x}
+  \end{align*}
+
+  \begin{enumerate}
+    \item Two possible outcomes: \textbf{success} or \textbf{failure}
+    \item \(\Pr(\text{success})\) is constant across trials (also denoted \(p\))
+    \item Finite number \(n\) of independent trials
+  \end{enumerate}
+
+  If these conditions are met, then it is a Binomial Random Variable. This variable is said to have a \textit{binomial probability distribution}.
+
+  \begin{itemize}
+    \item \(n\) is the number of trials
+    \item There are two possible outcomes: \(S\) or \(F\)
+    \item \(\Pr(\text{success}) = p\)
+    \item \(\Pr(\text{failure}) = 1-p = q\)
+    \item Shorthand notation: \(X \sim \operatorname{Bi}(n,p)\)
+  \end{itemize}
+
+  \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)
+

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