The GATE Grind

GATE 2022 ST – Question 16

Stochastic Processes · Markov Chains · 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?

  1. Both have unique stationary distributions.
  2. P₁ unique,P₂ infinitely many.
  3. P₁ infinitely many,P₂ unique.
  4. Neither has a unique stationary distribution.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) P₁ infinitely many,P₂ unique.

Explanation

P₁ has two absorbing states;any probability mixture of their point masses is stationary,so there are infinitely many. P₂ is irreducible:all states communicate through its positive transitions. Every finite irreducible chain has a unique stationary distribution. **C**.

More Markov Chains questions

All Markov Chains questions →