Consider the query P (Rain?Sprinkler = true, Wet-Grass = true) in Figure (a) and how MCMC can answer it.

a. How many states does the Markov chain have?

b. Calculate the transition matrix Q containing q (y ? y?) for all y. y?.

c. What does Q², the square of the transition matrix, represent?

d. What about Q ⁿ as n ???

e. Explain how to do probabilistic inference in Bayesian networks, assuming that Q? is available. Is this a practical way to do inference?

P(C)=5 Cloudy P(C)-5 CPIS CPIR) Clotudy Sprinkler Rain .10 .80 P(S+R=1) .20 Wet Grass .08 02 ,72 ,18 S10 ,40 ,10 40 Spr+Rain S+R P(W) SR P(W 99 99 Wet Grass 90 If .90 90 .00 90 .00 (b) (a) 10-0-C