Consider a continuous-time Markov chain with three states 1, 2, 3, 4, 5 and transition rates q12=1, q13 = 2, q21 = 0, q23 = 3, q31 = 0, q32 = 0. (1) Write the system of ODEs for the corresponding transition probabilities Pᵢⱼ (t) . (2) Suppose that the initial state is 1. What is the probability that after the first transition, the process X(t) enters state 2?