Consider the situation in Exercise 2, point b). Does the steady state probabilities solve the following set of equations? 0.7T0 +0.371+0.172 = T0 0.2то + 0.5л]+0.4тэ — T1 | To + T1+ 72 =1 no yes...

Mm4

Extracted text: Consider the situation in Exercise 2, point b). Does the steady state probabilities solve the following set of equations? 0.7T0 +0.371+0.172 = T0 0.2то + 0.5л]+0.4тэ — T1 | To + T1+ 72 =1 no yes Exercise 2: Using certain criteria the stock marked has what could be called a bad day (state 0), an average day (state 1) or a good day (state 2). Let X, be the state on day n. The process {X,: n = 0, 1, 2, 3, . } is assumed to be a Markov chain with the following transition matrix, Y 0.7 0.2 0.1 P = 0.3 0.5 0.2 0.1 0.4 0.5 and with 0.56 0.28 0.16) p² 0.38 0.39 0.23 0.24 0.42 0.34 a) Find P(X1 2|Xo 0), P(X4 1|X3 0, X2 = 1), P(X2 = 1|X, = 1) and %3D %3D %3D %3D %3D P(X21 = 1|X19 = 2). (Wait with point b) below until you have learned about steady state probabilities) b) Find the steady state (equilibrium) equations for this system and solve them. If the system starts in Xo = 0, what is the probability that P(X,= 0|Xo = 0) when n becomes large? %3D %3D