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A transition matrix is a square matrix used to describe the transitions of a Markov chain.
3
votes
Transition probabilities - Markov chains
I wouldn't have used Bayes' rule to solve this.
I would have computed $P(Y_1 = 1| Y_2=2)$ times $P(Y_1=1|Y_0=3)$. Then divide that for $P(Y_2=2|Y_0=3)$ computed using Chapman-Kolmogorov equation, I …