

\subsection{\bf Bernoulli Trials II}

\begin{slide}
\begin{itemize}
\item $b(k,n,p)$ is easily calculated by writing out all possible
outcomes as, for instance,
\[
\underbrace{ht\, h\, tt \ldots}_n
\]

\item There are $\left( \begin{array}{l} n \\ k \end{array} \right)$
configurations with $k$ ``$h$'' 's and each has probability $p^k
q^{n-k}$.  So:
\begin{equation}
b(k,n,p) = \left( \begin{array}{l} n \\ k \end{array} \right) p^k q^{n-k}
\end{equation}

\item This is the binomial distribution because $b(k,n,p)$ are just terms in
binomial expansion
\[
1 = (p+q)^n = \sum^n_{k=0} b(k,n,p).
\]
\end{itemize}
\end{slide}

