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\documentclass{article}\usepackage{amsmath, amssymb}\usepackage[english]{babel}\newcommand{\for}{\text{for }}\begin{document}\begin{align*}p^{00}_{p p'}&=\begin{cases}e^{-\lambda h}\,P_0(p'|p, n)& \for p_t\leq p_B (a_t=0)\\e^{-\lambda h}\,P_0(p'|p=0, n) & \for p_t>p_B (a_t=1)\end{cases}\\p^{01}_{p p'}&=\begin{cases}(1- e^{-\lambda h})\,P_1(p'|p, n)& \for p_t\leq p_B (a_t=0)\\(1-e^{-\lambda h})\,P_1(p'|p=0, n) & \for p_t>p_B (a_t=1)\end{cases}\\P^{10}_{p p'}&=\begin{cases}0 &\for p_t\leq p_B (a_t=0)\\e^{-\lambda h}\, P_0(p'|p=0, n) &\for p_t>p_B (a_t=1)\end{cases}\end{align*}\end{document}