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Markov Chains Practice

Master Markov chain theory with 10 comprehensive questions covering definitions, Chapman-Kolmogorov equations, state classification, stationary distributions, and applications.

10
Total Questions
0
Correct Answers
0
Questions Attempted
Basic Definition
1 questions
Question 1: Markov Property Definition
Which of the following correctly describes the Markov property?...
Beginner
Not attempted
Chapman-Kolmogorov Equations
1 questions
Question 2: Two-Step Transition Probability
Given a time-homogeneous Markov chain with transition matrix P = [[0.6, 0.4], [0.3, 0.7]], find p₀₁⁽...
Intermediate
Not attempted
Matrix Properties
1 questions
Question 3: Transition Matrix Properties
Which property of transition matrices is INCORRECT?...
Beginner
Not attempted
State Classification
2 questions
Question 4: Periodicity of States
Consider a Markov chain with states {0,1,2} and transitions p₀₁=1, p₁₂=1, p₂₀=1. What is the period ...
Intermediate
Not attempted
Question 5: Finite State Chain Properties
In finite state Markov chains, which statement about state types is correct?...
Advanced
Not attempted
Stationary Distributions
3 questions
Question 6: Stationary Distribution Relationship
For an irreducible, aperiodic, positive recurrent Markov chain with stationary distribution π, the r...
Intermediate
Not attempted
Question 8: Stationary Distribution Properties
Which statement about stationary distributions is correct?...
Advanced
Not attempted
Question 9: Computing Stationary Distribution
For a 2-state Markov chain with transition matrix P = [[0.8, 0.2], [0.3, 0.7]], the stationary distr...
Intermediate
Not attempted
Applications
2 questions
Question 7: Gambler's Ruin - Fair Game
In the gambler's ruin problem, player A starts with i=2 dollars, player B with m-i=3 dollars (total ...
Intermediate
Not attempted
Question 10: PageRank Algorithm
In the PageRank algorithm, which statement is correct?...
Advanced
Not attempted

Ready to Start?

Test your understanding of Markov chains with these challenging questions.