4.5. A chemical solution contains N molecules of type A and an equal number of molecules of type B. A reversible 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 ah + o(h), where a is a reaction rate of formation. Suppose also that in any small time interval of length h, any particular AB molecule disassociates into its A and B constituents with probability j3h + o(h), where

,6 is a reaction rate of dissolution. Let X(t) denote the number of AB molecules at time t. Model X(t) as a birth and death process by specifying the parameters.