Show that the statement P (A, B│C) = P (A│C) P (D│C) is equivalent to either of the statements P (A│B, C) = P (A│C) and P (B│A, C) = P (B│C).
Answer to relevant QuestionsSuppose you are given a bag containing n unbiased coins. You are told that n — 1 of these coins are normal, with heads on one side arid tails on the other, whereas one coin is a fake, with heads on both sides.a. Suppose ...(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 ...Consider the family of linear Gaussian networks, as illustrated.a. In a two-variable network, let X1 he the parent of X2, let X1 have a Gaussian prior, and let P (X2, X1) be a linear Gaussian distribution. Show that the ...Show that any second-order Markov process can be rewritten as a first-order Markov process with an augmented set of state variables. Can this always he done parsimoniously that is, without increasing the number of parameters ...Consider applying the variable elimination algorithm to the umbrella DBN unrolled for three slices, where the query is P( R3│U1,U2,U3), Show that the complexity of the algorithm—the size of the largest factor—is ...
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