Just had a quick question regarding the covariance between two dependent poisson distributions with stochastic intensity.
Say we have P_A which is distributed as Poi(aG) where a is constant and G is Gamma(a,b)
We also have P_B which is distributed as Poi(bG) where b is a constant.
Then how do we work out Cov(P_A, P_B)?
I have tried the conditional covariance formula but still cannot obtain Cov(P_A, P_B | G).
Any help would be much appreciated.