Question

Problem 1. Let {X_n} be a Markov chain in the state space S = {1, 2, 3} having the transition probability matrix P = |0.2 0.2 0.6| |0.7 0.3 0 | | 0 0.4 0.6| and the initial distribution p1 = P{X_0 = 1} = 0.5; p2 = P{X_0 = 2} = 0.3; p3 = P{X_0 = 3} = 0.2. Compute (a) P{X_0 = 1, X_1 = 3, X_2 = 2} (b) P{X_0 = 1, X_2 = 2} (c) P{X_3 = 2|X_1 = 3} (d) P{X_6 = 1, X_4 = 2, X_3 = 2, X_1 = 1|X_0 = 2} (e) P{X_6 = 1, X_4 = 2, X_3 = 2, X_1 = 1, X_0 = 2}

          Problem 1.
Let {X_n} be a Markov chain in the state space S = {1, 2, 3} having the transition probability matrix
P = |0.2 0.2 0.6|
    |0.7 0.3  0 |
    | 0  0.4 0.6|
and the initial distribution p1 = P{X_0 = 1} = 0.5; p2 = P{X_0 = 2} = 0.3; p3 = P{X_0 = 3} = 0.2. Compute
(a) P{X_0 = 1, X_1 = 3, X_2 = 2}
(b) P{X_0 = 1, X_2 = 2}
(c) P{X_3 = 2|X_1 = 3}
(d) P{X_6 = 1, X_4 = 2, X_3 = 2, X_1 = 1|X_0 = 2}
(e) P{X_6 = 1, X_4 = 2, X_3 = 2, X_1 = 1, X_0 = 2}

Problem 1.
Let Xn be a Markov chain in the state space S = 1, 2, 3 having the transition probability matrix
P = |0.2 0.2 0.6|
|0.7 0.3 0 |
| 0 0.4 0.6|
and the initial distribution p1 = PX0 = 1 = 0.5; p2 = PX0 = 2 = 0.3; p3 = PX0 = 3 = 0.2. Compute
(a) PX0 = 1, X1 = 3, X2 = 2
(b) PX0 = 1, X2 = 2
(c) PX3 = 2|X1 = 3
(d) PX6 = 1, X4 = 2, X3 = 2, X1 = 1|X0 = 2
(e) PX6 = 1, X4 = 2, X3 = 2, X1 = 1, X0 = 2

Added by April O.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Shaiju T

06/15/2022

Step 1

- The Markov chain has three states: {1, 2, 3}. - The transition probability matrix \( P \) is given as: \[ P = \begin{bmatrix} 0.2 & 0.2 & 0.6 \\ 0.7 & 0.3 & 0 \\ 0.4 & 0.6 & 0 \end{bmatrix} \] where \( P_{ij} \) is the probability of moving from Show more…

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Problem 1. Let {Xn} be a Markov chain in the state space S = {1, 2, 3} having the transition probability matrix P = 0.2 0.2 0.6 0.7 0.3 0 0 0.4 0.6 and the initial distribution p1 = P{X0 = 1} = 0.5; p2 = P{X0 = 2} = 0.3; p3 = P{X0 = 3} = 0.2. Compute (a) P{X0 = 1, X1 = 3, X2 = 2} (b) P{X0 = 1, X2 = 2} (c) P{X3 = 2|X1 = 3} (d) P{X6 = 1, X4 = 2, X3 = 2, X1 = 1|X0 = 2} (e) P{X6 = 1, X4 = 2, X3 = 2, X1 = 1, X0 = 2}