Markov Chain Quiz

Consider a Markov chain with two states, A and B. The transition matrix is given by:

[ 0.7 & 0.3 ]

0.4 & 0.6

What is the probability of transitioning from state A to state B?

• 0.7

• 0.3

• 0.4

• 0.6

Given the transition matrix: \[ \begin{bmatrix} 0.5 & 0.5 \\ 0.2 & 0.8 \\ \end{bmatrix} \] What is the probability of staying in state B once you are in state B?

• 0.2

• 0.5

• 0.8

• 0.5

A Markov chain has three states: X, Y, and Z. The transition matrix is: \[ \begin{bmatrix} 0.2 & 0.5 & 0.3 \\ 0.3 & 0.4 & 0.3 \\ 0.4 & 0.1 & 0.5 \\ \end{bmatrix} \] What is the probability of moving from state Y to state X?

• 0.3

• 0.4

• 0.1

• 0.5

If the transition matrix for a Markov chain is: \[ \begin{bmatrix} 0.9 & 0.1 \\ 0.6 & 0.4 \\ \end{bmatrix} \] What is the probability of transitioning from state B to state A?

• 0.1

• 0.4

• 0.6

• 0.9

Consider a Markov chain with the following transition matrix: \[ \begin{bmatrix} 0.3 & 0.7 \\ 0.8 & 0.2 \\ \end{bmatrix} \] What is the probability of transitioning from state A to state A?

• 0.3

• 0.7

• 0.8

• 0.2

Given a Markov chain with this transition matrix: \[ \begin{bmatrix} 0.6 & 0.4 \\ 0.5 & 0.5 \\ \end{bmatrix} \] What is the probability of transitioning from state B to state B?

• 0.5

• 0.4

• 0.6

• 0.5

A Markov chain has a transition matrix: \[ \begin{bmatrix} 0.1 & 0.9 \\ 0.7 & 0.3 \\ \end{bmatrix} \] What is the probability of moving from state B to state A?

• 0.7

• 0.3

• 0.1

• 0.9

The transition matrix for a Markov chain is: \[ \begin{bmatrix} 0.2 & 0.8 \\ 0.3 & 0.7 \\ \end{bmatrix} \] What is the probability of staying in state A once you are in state A?

• 0.2

• 0.8

• 0.3

• 0.7

Given the transition matrix: \[ \begin{bmatrix} 0.4 & 0.6 \\ 0.9 & 0.1 \\ \end{bmatrix} \] What is the probability of transitioning from state B to state A?

• 0.1

• 0.9

• 0.4

• 0.6

A Markov chain has the following transition matrix: \[ \begin{bmatrix} 0.5 & 0.5 \\ 0.6 & 0.4 \\ \end{bmatrix} \] What is the probability of moving from state A to state B?

• 0.5

• 0.4

• 0.6

• 0.5