Question

Determine whether or not the following matrices can be transition matrix for a Markov chain and explain why.

Answer 1

Al matrix is said to be transition matrix for a Markov chain, if the following condition hold i) It should be a square matrix (1) All the elements inside the matrix should be non- negative (zo) ii) Row sum should be equal to 1. NOW we will check the condition one by one (0) Toos 0 1 lo o.s . i) It is a square matrix ii) All the elements are no (non-negative) iii) ROW sum is not equal to 1. ie oost 0 = o.s 71 o tous = o.5 7 1 so it is not a transition matrix (6) 213 113 1 і т і, а кque ma_4 -сіх All the elements are z o (non-negative) ROW sum is equal to 1. i) 1 + 0 = 1

All the three conditions are satisfied so it is a transition marrin. It is a transition madrin. (c) 10.25 0.75 l loos oos ;) It is a square matrix 1 All the elements are 7o. (non-negative) iii) ROW seem is equal to 10 nie 0.25 & D.TS = 1 0.5 tous = 1 All the three conditions are satisfied so it is a transition matrix. (a) nos a transition matrix (3) & (E) are transition matrix