# Question: Consider the query P Rain Sprinkler true Wet Grass t

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?

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?

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