(Adapted from Pearl (1988)) Three prisoners, A, B, and C, are locked in their cells. It is common knowledge that one of them will be executed the next day and the others pardoned. Only the governor knows which one will be executed. Prisoner A asks the guard a favor. “Please ask the governor who will be executed, and then take a message to one of my friends B or C to let him know that he will be pardoned in the morning.” The guard agrees, and comes back later and tells A that he gave the pardon message to B. What are A’s chances of being executed, given this information? (Answer this mathematically, not by energetic waving of hands.)
Answer to relevant QuestionsWrite out a general algorithm for answering queries of the form P (Cause│e), using a naive Bayes distribution. You should assume that the evidence e may assign values to any subset of the effect variables.e. What is the most likely number of stars, given these observations? Explain how to compute this, or, if it is not possible to compute, explain what additional information is needed and how it would affect theresult.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 → ...Let us examine the behavior of the variance update in Equation (15.1). a. Plot the value of σ2t as a function of t, given various values for σ2x and σ2z. b. Show that the update has a fixed point u σ2 ...Write a computer program to automate the process in Exercise 16.4. Try your program out on several people of different net worth and political outlook. Comment on the consistency of your results, both for an individual and ...
Post your question