=+12. Suppose Xn denotes the number of particles in a branching process with immigration. Let be

=+12. Suppose Xn denotes the number of particles in a branching process with immigration. Let μ be the mean number of progeny per particle and α the mean number of new immigrants per generation. An ordinary branching process corresponds to the case α = 0. For k>j show that E(Xk | Xj) = 3 (k − j)α + Xj , μ = 1

α(1−μk−j )

1−μ + μk−jXj, μ = 1 Cov(Xk, Xj) = μk−j Var(Xj ).