 Serial reaction dwell-time density

Two sequential independent memoryless reaction waits have a hypoexponential distribution. Convolution gives $p(t)=k_1{k}_2(e^{-k_{1}t}-e^{-k_{2}t})/(k_2-k_1)$. Equal rates give the Erlang distribution $k^{2}t{e}^{-kt}$. A nonzero mode distinguishes this ideal two-event model from a single exponential wait, but does not chemically identify the events.