Question

Consider a Markov chain with state space {0, 1, 2, 3} and transition matrix P = ( 0.5 0.5 0 0 0.2 0.8 0 0 0.3 0.5 0.1 0.1 0 0.3 0.3 0.4 ). Suppose that the Markov chain starts in state 3. (a) Find the expected number of time periods that the Markov chain is in state 3. (b) Find the probability that the Markov chain ever makes a transition into state 2. (c) Find the probability that the Markov chain ever makes a transition into state 0.

          Consider a Markov chain with state space {0, 1, 2, 3} and transition matrix
P = (
0.5 0.5 0 0
0.2 0.8 0 0
0.3 0.5 0.1 0.1
0 0.3 0.3 0.4
).
Suppose that the Markov chain starts in state 3.
(a) Find the expected number of time periods that the Markov chain is in state 3.
(b) Find the probability that the Markov chain ever makes a transition into state 2.
(c) Find the probability that the Markov chain ever makes a transition into state 0.

Consider a Markov chain with state space 0, 1, 2, 3 and transition matrix
P = (
0.5 0.5 0 0
0.2 0.8 0 0
0.3 0.5 0.1 0.1
0 0.3 0.3 0.4
).
Suppose that the Markov chain starts in state 3.
(a) Find the expected number of time periods that the Markov chain is in state 3.
(b) Find the probability that the Markov chain ever makes a transition into state 2.
(c) Find the probability that the Markov chain ever makes a transition into state 0.

Added by Amanda C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Maitreya T

03/05/2022

Step 1

It seems like it's a 4x4 matrix, but the provided numbers don't match up. A 4x4 matrix should have 16 entries, but only 11 are provided. Let's assume the transition matrix is as follows: P = [0.5 0.5 0; 0.2 0.3 0.5; 0.1 0.1 0.3; 0.2 0.1 0.4] This matrix Show more…

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Consider a Markov chain with state space {0, 1, 2, 3} and transition matrix P = ( 0.5 0.5 0 0 0.2 0.8 0 0 0.3 0.5 0.1 0.1 0 0.3 0.3 0.4 ). Suppose that the Markov chain starts in state 3. (a) Find the expected number of time periods that the Markov chain is in state 3. (b) Find the probability that the Markov chain ever makes a transition into state 2. (c) Find the probability that the Markov chain ever makes a transition into state 0.