Question

In Example 4.13, give the transition probabilities of the Yₙ Markov chain in terms of the transition probabilities πᵢⱼ of the Xₙ chain.

a) P(Yₙ = j | Yₙ₋₁ = i) = πᵢⱼ

b) P(Yₙ = i | Yₙ₋₁ = j) = πᵢⱼ

c) P(Yₙ = i | Xₙ = j) = πᵢⱼ

d) P(Yₙ = j | Xₙ = i) = πᵢⱼ

Answer 1

Without the specific context of Example 4.13, only a general discussion of transition probabilities in Markov chains can be provided. In Markov chains, transition probabilities quantify the likelihood of transitioning from one state to another within the chain.

Step-by-step explanation:

The question appears to be related to Markov chains and their transition probabilities. However, the reference to Example 4.13 is missing, making it challenging to provide a specific answer. In general, transition probabilities in a Markov chain describe the likelihood of moving from one state to another. If Yn and Xn are two Markov chains, their transition probabilities can be related depending on how these chains are defined relative to each other. The probability P(Yn = j | Yn−₁ = i) would represent the probability of transitioning from state i to state j in the Yn chain, and could potentially be expressed in terms of the πij of the Xn chain depending on the relationship between the two chains.