I am trying the write something below in latex and what I am trying seems not working well.
\documentclass[10pt,english,8pt]{beamer}
\usepackage{amsmath}
\begin{document}
\begin{frame}
\begin{itemize}
\item Observation equation:
$\begin{pmatrix}
PD_{s,t}\\
RR_{s,t}
\end{pmatrix} = \binom(\gamma_{1}\gamma_{2}) = bla
\end{itemize}
\end{frame}
\end{document}
The syntax \binom(...) is wrong. \binom is a macro with two mandatory arguments, so you need to write \binom{...}{...}.
Some other comments:
the closing $ is missing
personally I would use the pmatrix in both cases to get a more uniform result
combining the 10pt and 8pt class options makes not much sense, they are mutually exclusive. Decide which of the two options you want and then use only this option, not both
you don't need to load amsmath, beamer loads it automatically
\documentclass[english,8pt]{beamer}
\begin{document}
\begin{frame}
\begin{itemize}
\item Observation equation:
$\begin{pmatrix}
PD_{s,t}\\
RR_{s,t}
\end{pmatrix} = \binom{\gamma_{1}}{\gamma_{2}} = bla
$
\end{itemize}
\end{frame}
\end{document}
