GATE 2023 ST – Question 34

Stochastic Processes · Markov Chains · 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.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 0.36 to 0.39

Explanation

By the Markov property,the numerator is p₁₁p₁₂=1/8. The denominator (P²)₁₂=(1/2)(1/4)+(1/4)(1/3)+(1/4)(1/2)=1/3. Their ratio is 3/8=0.375,rounded **0.38**.

More Markov Chains questions

GATE 2022 ST Q16 – 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)…
GATE 2022 ST Q34 – If a company pays a quarterly dividend,the next is paid with probability .7. If it stops a…
GATE 2022 ST Q57 – At each repeated food experiment,70% of cats previously eating A choose A,and 50%…
GATE 2021 ST Q30 – A Markov chain on 0,1 has transition rows (.25,.75),(.75,.25),and P(X₀=0)=P(X₀=1)=.5. Find…
GATE 2021 ST Q46 – A time-homogeneous discrete Markov chain has finite or countable state space S. Which…
GATE 2026 ST Q18 – A homogeneous Markov chain on 1,…,7 has transition matrix…

All Markov Chains questions →