calculate the steady state probability of source emitting a "0"

from "Applied coding and information theory for engineers"
page 70, chapter 2, example 2.4.4

pi0=1/9
pi1=pi2=2/9
pi3=4/9

For Pr(0) how are the values for Pr(0/Sn) found,
by my observation, Pr(0/S3) should be 0 but its 0.5 why?

thanks

To calculate the steady-state probability of the source emitting a "0", we need to find the probability of being in state S3 (Sn = S3) and emitting a "0". According to the provided information, the probabilities for being in each state are:

pi0 = 1/9
pi1 = pi2 = 2/9
pi3 = 4/9

To find Pr(0/S3), we need to determine the probability of emitting a "0" when in state S3.

In example 2.4.4 on page 70 of "Applied coding and information theory for engineers," it is mentioned that the system transitions between states according to a Markov chain. However, it is not explicitly stated how the emission probabilities are related to the states. Therefore, we need to make an assumption or clarification to proceed.

If we assume that the emission probabilities are independent of the state and remain constant regardless of the current state, then Pr(0/S3) should indeed be 0.5 as you initially observed.

However, if there is additional information or if it is clarified in the textbook that the emission probabilities are dependent on the state, then we would need that information to accurately determine the value of Pr(0/S3).