Question

Consider the Markov chain with three states S = {1, 2, 3} and probability distribution at time t = 0 given by $\pi^{(0)} = [0.2 \quad 0.3 \quad 0.5]$ a) Write the state transition matrix for this chain using the given state transition diagram. b) Find $P(X_1 = 1 \mid X_0 = 3)$ c) Find $P(X_0 = 1, X_1 = 2, X_2 = 3)$ d) Find $\pi^{(3)}$, and then write the probability that the system is in state 3 at time n = 3

          Consider the Markov chain with three states S = {1, 2, 3} and probability distribution
at time t = 0 given by $\pi^{(0)} = [0.2 \quad 0.3 \quad 0.5]$
a) Write the state transition matrix for this chain
using the given state transition diagram.
b) Find $P(X_1 = 1 \mid X_0 = 3)$
c) Find $P(X_0 = 1, X_1 = 2, X_2 = 3)$
d) Find $\pi^{(3)}$, and then write the probability that the system is in state 3 at time n = 3

Consider the Markov chain with three states S = 1, 2, 3 and probability distribution
at time t = 0 given by π^(0) = [0.2 0.3 0.5]
a) Write the state transition matrix for this chain
using the given state transition diagram.
b) Find P(X1 = 1 | X0 = 3)
c) Find P(X0 = 1, X1 = 2, X2 = 3)
d) Find π^(3), and then write the probability that the system is in state 3 at time n = 3

Added by Jose Ramon S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Maitreya T

03/05/2022

Step 1

The rows of the matrix represent the current state, and the columns represent the next state. The entries in the matrix are the probabilities of transitioning from the current state to the next state. Show more…

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Consider the Markov chain with three states S = {1, 2, 3} and probability distribution at time t = 0 given by π(0) = [0.2 0.3 0.5] a) Write the state transition matrix for this chain using the given state transition diagram. 0.1 2 1 0.9 0.4 1 3 b) Find P(X₁ = 1 | Xo = 3) 0.6 c) Find P (Xo = 1, X1 = 2, X2 = 3) d) Find π(3), and then write the probability that the system is in state 3 at time n = 3