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ml-recall

#conditional-probability-table

1 question from Probabilistic & Graphical Models

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Question 1: Short answer

easyAI-checkedProbabilistic & Graphical Models

In a Bayesian network, x4x_4 has parents x1x_1 and x2x_2 (all binary). Its table so far reads P(x4=1∣x1=0,x2=0)=0.8P(x_4 = 1 \mid x_1 = 0, x_2 = 0) = 0.8, P(x4=1∣x1=0,x2=1)=0.4P(x_4 = 1 \mid x_1 = 0, x_2 = 1) = 0.4 and P(x4=1∣x1=1,x2=0)=0.8P(x_4 = 1 \mid x_1 = 1, x_2 = 0) = 0.8. What must P(x4=1∣x1=1,x2=1)P(x_4 = 1 \mid x_1 = 1, x_2 = 1) be for the edge x1→x4x_1 \to x_4 to be removable without misrepresenting the distribution?

a probability