I recently asked this on Biology.SE, and need to start with the master equation for the reaction: $$\ce{E + S -> ES}$$ Where $\ce{E}$ is our enzyme and $\ce{S}$ the substrate to get a probability density function for the binding time of a substrate with one specific enzyme to be: $$f{\left(t\right)}=k\left[\ce{S}\right]\mathrm e^{-k\left[\ce{S}\right]t}$$ I have read up on master equations, but really have no idea where to start in this derivation, any help would be appreciated?