We propose an exactly solvable method to study the coherent two-colour photoassociation of an atomic BoseEinstein condensate,by linearizing the bilinear atom-molecule coupling,which allows su to conveniently probe the quantum dynamics and statistics of the system.By preparing different initial states of the atomic condensate,we can observe very different quantum statistical properties of the system by exactly calculating the quadraturesqueezed and mode-correlated functions.