Exercises 3.3.1Consider a spare parts inventory model in which either 0, 1, or 2 repair parts are demanded in any period, with Pr{n = 0} - 0.4 Pr {En = 1} - 0.3, Pr{En - 2} - 0.3, and suppose s = 0 and S = 3. Determine the transition probability matrix for the Markov chain {X,}, where X, is defined to be the quantity on hand at the end-of-period n. From the given information: Pr (5, = 0) = 0.4 Pr (5, =1) = 0.3 Pr (5,, = 2) =0.3 s = 0 and S = 3 The possible value of X, are: 3,2, 1,0,-1 Transition matrix probability can be calculated as: P, = Pr{ X,, = jIX, = 1} Pr(5, =i-j} ifs