Markov chain

Consider a Markov chain {Xn, n = 0, 1, . .. } on the state space S = {0, 1, 2}. Suppose that the Markov chain has the transition matrix 0 P = 1 0 0 NIH 1. Show that the state space is irreducible. 2. Show that the Markov chain is periodic. Find the period of the Markov chain. 3. Let h denote a stationary mass of the Markov chain. Find h(x) for all x E S.Question 3 Given the following statistics, calculate the lower Not yet bound for the 90% Confidence Interval for true answered average sleep (S): (3 significant digits in final Marked out of answer, use statistics table provided in eclass) 0.50 Sbar = 6.5 Flag sd(S)=1.2 question N=900 Answer:An aircraft flies at Mach 1.5 at 51000 ft (Pa=11 0KPa,To=216.7 K) propelled by a simple turbojet engine. The air enters the compressor and turbine at a rate of 20kg/s. (7=14,cp=1005J/{kg.Kj). a Find the stagnation temperature and pressure into the compressor, if the inlet is effectively isentropic. b. The engine compressor has a pressure ratio of 15 with an isentropic efficiency of 8516. Find the compressor work input. c. In the combustor the velocities are low (so the stagnation and static pressure are equal] with 596 pressure drop. At turbine entry the stagnation temperature is 1400 K and the turbine has an efficiency of 89%% and 65%% work output from turbine is used as compressor work input. Calculate the pressure ratio of the turbine and the thermal efficiency. d. If the final propelling nozzle is isentropic, find the velocity of the jet Subject on Gas Turbine Engines