b)
P(X1 = 2 , X2 = 2 , X3 = 1 |X0 = 1) = P12*P22*P21
= 0.4 * 0.75*0.25
= 0.075
c)
P^n when n tend to infinity =
0.2439
0.39024 0.36585
0.2439
0.39024 0.36585
0.2439
0.39024 0.36585
Let (X.) be a Marko chain with the state space (1.2,3) and transition proba- bility matrix...
10. Consider the Marko chain (X0,.) with state space (0,1,2,3,4) and transition matris 0.2 0. 0.4 0.3 0 01 0.4 0 0.2 0.3 P 0.3 0 0. 0.4 0.2 0.4 0.3 0.2 0.1 0 0.2 0.3 0. 0.4 Find P(X-3, X-4No 3)
3.1.4 The random variables ξ1.ξ2 are independent and with the common proba- bility mass function k= 0 1 2 3 Prk)0.1 0.3 0.2 0.4 Set Xo 0, and let x, max(ξι, . . . , ξη} be the largest ξ observed to date. Deter- mine the transition probability matrix for the Markov chain (Xn).
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Let Xn be a Markov chain with state space {0, 1, 2}, and transition probability matrix and initial distribution π = (0.2, 0.5, 0.3). Calculate P(X1 = 2) and P(X3 = 2|X0 = 0) 0.3 0.1 0.6 p0.4 0.4 0.2 0.1 0.7 0.2
Let Xn be a Markov chain with state space {0,1,2}, the initial probability vector and one step transition matrix a. Compute. b. Compute. 3. Let X be a Markov chain with state space {0,1,2}, the initial probability vector - and one step transition matrix pt 0 Compute P-1, X, = 0, x, - 2), P(X, = 0) b. Compute P( -1| X, = 2), P(X, = 0 | X, = 1) _ a. 3. Let X be a Markov chain...
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Let P be the n*n transition matrix of a Markov chain with a finite state space S = {1, 2, ..., n}. Show that 7 is the stationary distribution of the Markov chain, i.e., P = , 2hTi = 1 if and only if (I – P+117) = 17 where I is the n*n identity matrix and 17 = [11...1) is a 1 * n row vector with all components being 1.