3 Message Passing: BP Algorithm. VC)-1, their joint probability will be For 3 Boolean variables A, B, and C that satisfy the constraint (AVB)A( given by the following expression: P(A, B, C) = (A)d(B)(C)(A v B) ^ (AVC) where Z is a normalization constant. (A) is the prior probability for A, that says A will be equally likely to be 0 or 1 a priori, i.e., (A = 1) = (A = 0)-| . Similary, that is the case for (B) and (C). Note that V denotes logic operator OR and A AND (a) Draw a factor graph to represent the above joint probability P(A, B,C) b) Using a message passing algorithm (e.g, BP) to compute the marginal probability P(A)-BCP(A, B,C). In particular, what is P(A=1)? (c) Verify your results via exhaustive enumeration. (d) What is P(A = 1) if there are 4 Boolean variables and the constraint is (A v B)^ ( v D) = 1