[Tex/LaTex] How to write Exponential distribution in overleaf

Question

I am new to overleaf and having trouble in writing an exponential distribution function in overleaf.

Could anyone please help me share some insight on how to write it?
Thanks in advance!!

Answer 1

Use cases (or dcases), and although I prefer writing exp, if you insist on using e ensure it is an upright letter, as its a number, not a variable, so use \mathrm{e}.

\documentclass{article}
\usepackage{amsmath,mathtools}
\begin{document}
\begin{equation}
f_X(x) = 
\begin{cases}
\lambda \exp(-\lambda x) & x > 0 \\
0 & \text{otherwise.}
\end{cases}
\end{equation}
or
\begin{equation}
f_X(x) = 
\begin{dcases}
\lambda \mathrm{e}^{-\lambda x} & x > 0 \\
0 & \text{otherwise.}
\end{dcases}
\end{equation}
\end{document}