Solution
= Solution
Before the first product forms, the system is in either $E_0$ or $C_0$. Product formation is possible only through $C_0\to E_1$, so the <first-passage-time density> is the outgoing probability flux
$$
f(\tau)=k_2C_0(\tau)
=\frac{k_1k_2}{\lambda_+-\lambda_-}
\left(e^{-\lambda_-\tau}-e^{-\lambda_+\tau}\right),
\qquad \tau\geq0.
$$
Equivalently, the <survival function> is $E_0(\tau)+C_0(\tau)$ and its negative derivative is this density.