PROBABILITY AND STOCHASTIC PROCESS

QUESTION 4 Let X1 (t) and X2 (t) be two independent Poisson processes with rates , and A2 respectively (a) Is the process Y (t) = X1 (t) - X2 (t) a Markov process? If no, explain why If yes, explain why and describe its states and transition rates (7) (b) Which of the following statements are true and which are false? Justify your answers! (1) If X1 > 12 then Xi (t) > X2 (t) for all t (1) If A1 > >2 then P (X1 (t) > 0) > P(X2 (t) > 0) for all t (m) If X1 > >2 then E (X1 (t)) > E(X2 (t)) for all t