%defines the datalog operator :- with correct spacing etc.
%defines the program code minipage environment that I used with rules top and bottom
%NOTE: you will need to change the lift value for the \rule command. This is set fo 1.5 spacing.
%      single spacing: 6pt/6pt and doublespacing: 0pt and 12 point (I believe)
%NOTE: If you use a \tabbing environment immediately after \progstart, the follow progstart by \vspace{-18pt}


\documentclass[letterpaper]{article}
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\newtheorem{corollary1}{Corollary}
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\def\progend{\rm\rule[6pt]{\linewidth}{0.4pt} \\ \end{minipage}\end{center}}
\input{tcilatex}
\begin{document}


{\huge \noindent The binomial distribution gives the discrete probability
distribution $P_{p}(k|N)$ of obtaining exactly $k$ successes out of $N$
trials where the result of each trial is true with a probability of $p$ and
false with a probability of $q=1-p$. 
\begin{eqnarray}
P_{p}(k|n) &=&\binom{N}{k}p^{k}q^{N-k}, \\
&=&\frac{N!}{k!(N-k)!}p^{k}(1-p)^{N-k},
\end{eqnarray}%
where $\binom{N}{n}$ is a binomial coefficient. }

{\huge \pagebreak }

{\huge \noindent We can find $P=$ \textquotedblleft the probability that 10
or less users are active.\textquotedblright\ Then $1-P=$ \textquotedblleft\
the probability that more than 10 users are active.\textquotedblright\ We
find $P$ as 
\begin{equation}
\sum_{k=0}^{10}\binom{35}{k}p^{k}q^{N-k}
\end{equation}%
}

\end{document}
