GATE Stochastic Processes: Markov Chains – Previous Year Questions

10 GATE previous year questions on Markov Chains (Stochastic Processes, Statistics) with answers and explanations, from every paper.

1. GATE 2021 ST Q30 (1 mark, Numerical answer) – A Markov chain on 0,1 has transition rows (.25,.75),(.75,.25),and P(X₀=0)=P(X₀=1)=.5. Find Σ (k=1)100 E[(X (2k))(2k)].
2. GATE 2021 ST Q46 (2 marks, Multiple choice) – A time-homogeneous discrete Markov chain has finite or countable state space S. Which statement is true?
3. GATE 2022 ST Q16 (1 mark, Multiple choice) – Two Markov transition matrices have rows P₁:(1,0,0),(1/3,1/2,1/6),(0,0,1);P₂:(1/6,1/3,1/2),(1/4,0,3/4),(0,1,0). Which holds?
4. GATE 2022 ST Q34 (1 mark, Numerical answer) – If a company pays a quarterly dividend,the next is paid with probability .7. If it stops a dividend,the next is not paid with probability .5. Find the…
5. GATE 2022 ST Q57 (2 marks, Numerical answer) – At each repeated food experiment,70% of cats previously eating A choose A,and 50% previously eating B choose A. Initially 40% ate A in experiment 1.…
6. GATE 2023 ST Q34 (1 mark, Numerical answer) – A Markov chain on 1,2,3 has transition rows (1/2,1/4,1/4),(1/3,1/3,1/3),(0,1/2,1/2). Find P(X₂=1 X₁=1,X₃=2),to two decimals.
7. GATE 2024 ST Q53 (2 marks, Multiple select) – A chain on 0,1,2 has P=pmatrix1/2&1/2&0\\1/2&1/2&0\\1/3&1/3&1/3pmatrix. Which hold?
8. GATE 2024 ST Q60 (2 marks, Numerical answer) – A chain on 0,1,2 has P=pmatrix0&1/2&1/2\\1/2&1/4&1/4\\1/2&1/4&1/4pmatrix and initial probabilities P(X₀=0)=P(X₀=1)=1/4. Find 32E(X₂) (integer).
9. GATE 2025 ST Q51 (2 marks, Multiple select) – A Markov chain on 1,2,3 has P=pmatrix0&1/2&1/2\\1/3&0&2/3\\2/5&3/5&0pmatrix and π=(18,24,25)/67. Which hold?
10. GATE 2026 ST Q18 (1 mark, Multiple choice) – A homogeneous Markov chain on 1,…,7 has transition matrix P=pmatrix1/3&0&2/3&0&0&0&0\\0&1/3&0&1/3&0&1/3&0\\1/2&0&1/2&0&0&0&0\\0&1/2&0&1/4&0&1/4&0\\1/2…