6.2.4 A chemical solution contains N molecules of type A and M molecules of type B. An irreversible reaction occurs between type A and B molecules in which they bond to form a new compound AB. Suppose that in any small time interval of length h, any particular unbonded A molecule will react with any particular unbonded B molecule with probability hCo.h/, where  is a reaction rate. Let X.t/ denote the number of unbonded A molecules at time t.

(a) Model X.t/ as a pure death process by specifying the parameters.

(b) Assume that N < M so that eventually all of the A molecules become bonded. Determine the mean time until this happens.