Question 5 (6 points): Purpose: A few more complicated calculations, to make the

Question

Question 5 (6 points): Purpose: A few more complicated calculations, to make the formula concrete The following diagram represents a simple, 4 node Bayesian Network. The nodes represent outcomes F, S, T, A. The Conditional Probability Distributions (CPDs) for these nodes are as follows P(7-0) P(7-1) 001 0.99 P(F-1) 0.99 P(S-OF-0.9 Ps-11F-0) -0.1 P(S-0F-1) -O.OI P(A-1 F-1,T-0) 0.15 P(A-1F-1,T-1) 0.9999 Using this information, answer the following questions (a) Calculate P(A=0|F-0). Hint: Which nodes are not relevant to the query? (b) Calculate P(F-0S-0). Hint: Which nodes are not relevant to the query? (c) Calculate P(A-01S=0). Hint: Which nodes are not relevant to the query? Hopefully you have the idea that numbers can make calculations seem less abstract, but they don't actu- ally buy us anything, and they're a pain in the neck. From now on, we'lljust do the algebra

Explanation / Answer

Ans a. P(A=0| F=0)= P(A=0 U F=0)/P(F=0)                        Let U = intersection

                              = 0.5 * 0.01/0.01 = 0.5

S not relevant to the query

Ans b. P(F=0| S=0)= P(F=0 U S=0)/P(S=0)

                             = 0.9

T not relevant to the query.

Ans c. P(A=0| S=0)= P(A=0 U S=0)/P(S=0)

                             =

T not relevant to the query.

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