Let xt t ge 0 and ytt ge 0 be independent poisson processes

Question

Let {X(t), t ≥ 0} and {Y(t),t ≥ 0} be independent Poisson processes with parameters λ1 and λ2, respectively. Define Z1(t) = X(t) + Y(t), Z2(t) = X(t) - Y(t), Z3(t) = X(t) + k, k a positive integer. Determine which of the above processes are Poisson and find λ.