PSet 18: Markov Chains

(videos: Markov Models and Chain Example)

1. Given the following transition probabilities for a markov chain, what is the probability distribution at X3? Assume the first node is X1 like so: X1 -> X2 -> X3

   Show your work on the right and fill in the two blanks at the bottom.

   
   

   $P(X_1=a) = 0.9$
   $P(X_1=b) = 0.1$

   
   

   And the transition probabilities:

P(X3=a) = ___________

P(X3=b) = ___________

2. Given the following transition probabilities of a markov chain, what is the stationary distribution?

P(X=a) = ___________

P(X=b) = ___________

3. Given the following transition probabilities of a markov chain, what is the stationary distribution?

P(X=c) = ___________

P(X=d) = ___________