The number of messages residing in a processing system at time t is recordedanddenoted as X(t). Its dynamic evolution over time t is modeled as a continuous-time birth-anddeath Markov Chain X = {X(t), t 0}, over the state space S = {0,1,2}. The processischaracterized by the following intensities: q01 = 1.25 [1/sec.]; q10 = 0.32 [1/sec.]; q12 =0.48[1/sec.]; q21 = 0.8 [1/sec.]. a. Calculate the average time that the process stays in each state before transitioningtoanother state. b. Obtain the transition probability matrix R of the embedded state sequence Y. c. Calculate the steady-state probability that at a given time in steady-state the systemwill be empty (i.e., reside at state 0). d. Calculate the average time that it takes the system to transition fromstate 0backtostate 0 (i.e., the average time elapsed from the instant that the systementers state0tothe time that it subsequently enters