Continuous time Markov chain.

Please help me with part (3). If you can't solve it, please leave to other tutors. Thank you!

Q. 3 (14 points). Let (Xt)to be a continuous-time Markov chain with four states, {1, 2, 3, 4}. The transition rates of X are given by the following diagram: 2 1 2 1 2 4 2 3 X2= 3 (1) Identify the rate matrix of X. (2) If the first (initial) state of the process is Xo = 1, find the probablety that the third state visited by the process is 3. (3) Starting from Xo = 1, find the probability that the process is in state 3 at time t = 2.5. Give an answer accurate to 3 decimal places