Hi there people! Im doing a project based on predicting Football (soccer) results but have hit a slight roadblock when investigating the dependance between the goals scored by the home and away team.

Im modelling the goals scored using the poisson distribution as follows:

H = C + Eh

A = C + Ea

C is independent with H, A, Eh and Ea. H and A are also independent.

Where C is poisson distributed with mean Theta, Eh is poisson distributed with mean (Lambda-Theta) and Ea is poisson distributed with mean (Mu-Theta).

Now, my question is, how woud I calculate the probability H=1,A=1.

Would appreciate any help I could get, my stats isnt too great to be honest. Thanks in advance.