A chemical solution contains $N$ molecules of type A and $M$ molecules of type B. An irreversible reaction occurs between type A and type B molecules in which they bond to form a new compound AB. Suppose that in any small time interval of length h, any particular unbounded A molecule will react to any particular unbounded B molecule with probability $\theta h + o(h)$ where theta is a reaction rate. Let $X(t)$ denote the number of unbounded A molecules at time $t$.
Model $X(t)$ as a pure death process by specifying parameters.
$k ( M - (N-k) ) \theta$ for $k = 0, 1, 2, ... , N$, this is the answer and what is the hints to get it?
Assume that N < M so that eventually all of the A molecules become bonded. Determine the mean time until this happens.
For finding the mean time, we need to take the integral from zero to infinity, but what we need to integral?