Question: A population of organisms consists of both male and female members. In a small colony any particular male is likely to mate with any particular female in any time interval of length h, with probability \(\lambda h+o\left( h \right)\). Each mating immediately produces one offspring, equally likely to be male and female. Let \({{N}_{1}}\left( t \right)\) and \({{N}_{2}}\left( t \right)\) denote the number of males and females at time t. Derive the parameters of the continuous-time Markov chain \(\left\{ {{N}_{1}}\left( t \right),{{N}_{2}}\left( t \right) \right\}\), i.e. the \({{v}_{i}}\) and \({{P}_{ij}}\)