Vs Figure 1: The Bayesian network for Problem 1.2. Problem 1.2, Bayesian networks Consider the Bayesian network in the f

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Vs Figure 1 The Bayesian Network For Problem 1 2 Problem 1 2 Bayesian Networks Consider The Bayesian Network In The F 1 (65.17 KiB) Viewed 199 times

Vs Figure 1: The Bayesian network for Problem 1.2. Problem 1.2, Bayesian networks Consider the Bayesian network in the figure above. In this case, the network contains five random variables (V1 V2 V3,VA, and V:). The variables take binary values, i.e. either true or false Making use of the conditional independence relations implied by the network structure, write the expression for the full joint probability distribution P(V.V.V.V.V:) as a product of condi- tional probabilities. Then determine how many parameters are required in order to fully specify the distribution (1) I 0.1 (2) Next, assume that the following conditional probability tables (CPT) are known P(V = true) =0.5 =false P(V> = truelv;) = { 0.95 if Vi true P(V; = true|Vi) = { 0.8 if Vi = false 0.5 if Vi = true 0.1 if V; = false and V = false s 0.9 P(V. = true V1V2) if Vi = true and V2 = false 0.3 if Vi = false and V = true 0.95 if Vi = true and V, = true P(Vs = trueV) = [ 0.8 if V = false 0.1 if V4 = true Making use of the structure of the network and the CPT), compute (i) P(Vi =true. V =true, Vs =true, Vi=true, Vs =true), and (ii) P(Vs =true Vi=true). (4) (5)