I recently asked [this on Biology.SE][1], 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?


  [1]: https://biology.stackexchange.com/questions/38576/dwell-time-equations-for-atp-sythase?noredirect=1