A birth-death process has 3 states: {0, 1, 2}. It is defined by 0 = 0, 1 = 1, 2 = 2, 0 = 2, 1 = 1.5, 2 = 0. . Write down the generator matrix. b. Write down both the backward and the forward differential equation for 1,2 (). c. Let = Time that takes the system to move from state to state + 1. Find (1) ( You will need to calculate first (0) ). d. Find the steady state distribution of the system (use balance equations).