An elevator starts in the basement and travels upward. We denote N_i the number of people who get in the elevator at floor i for i 0, and assume that N_is are independent and each N_i is Poisson distribution with mean _i. Each person entering at floor i will get off at floor j with probability p_{ij} , independent of everything else, satisfying sum_{j>i} p_{ij} = 1. Finally, we denote D_j the number of people getting off the elevator at floor j. (a) Find the expression of E[D_j]. (b) What is the joint distribution of D_j and D_k for j != k?.