Question 4 (6 points) Purpose: Simple calculations as a warm-up The following diagram represents a simple, 2 node Bayesian Network. The nodes represent outcomes F and S. The Conditional Probability Distributions (CPDs) for these nodes are as follows: P(F-0)-0.01 P(S-1F-0.1 P(S-1F-1)0.99 Using this information, answer the following questions. (a) Calculate P(S-0F-0). Hint: Look up the value in the CPD. (b) Calculate s P(SF-0) (c) Calculate P(F-0). Hint: Look up the value (d) Calculate s P(SF-0) P(F-0). Use your calculations from previous steps. This is what we mean when we say S is irrelevant. The rule for irrelevance in a Bayesian network allows us to leave out variables that just will not affect the answer. If you leave irrelevant variables in your calculations, you get the same answer, but you do more work. (e) Calculate P(F-0S-0). Use Bayes Rule. Pay attention specifically to the denominator ( Calculate P(F-11s-0). Use Bayes Rule. Pay attention specifically to the denominator Notice the similarity in the formulae of this answer and the previous answer. This is why we prefer to derive a symbolic formula, e.g. P(FIS): the same formula can be applied to any outcome for F or S