

\subsection{\bf Basic Birth Process Formalism---I}

\begin{slide}
\begin{itemize}
\item It is natural to take limit of time interval (second in above example)
as zero, and let $t$ be a continuous and not a discrete valued
variable.  

\item Suppose we are studying events (e.g., telephone calls as
above) that 

\begin{description}
\item{$\bullet$} $\alpha)$ occur independently of previous history of
world, 
\item{$\bullet$}
$\beta)$ in time $[t,t+dt]$. 

\begin{description} 
\item{$\bullet$} The probability of an event happening is $\lambda dt +
o(dt)$,
\item{$\bullet$} and the probability of $>1$ event happening is $o(dt)$.
\end{description}
\end{description}

\item Define $P_k(t)$ as the probability of $k$ events happening in
time 0 to $t$.
\end{itemize}
\end{slide}
