\documentclass[12pt]{article}

\newenvironment{LRmath}{
  \def\E{}
  \renewcommand{\E}[2][]{\ensuremath\mathrm{E}_{##1}\!\left[##2\right]}
  \def\PP{\ensuremath\mathrm{P}}
}{}

\begin{document}
\begin{equation}
    \PP[x\le y] = \E[x]{\max(y-x,0)/(y-x)}
\end{equation}
\end{document}
