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Bayesian Network

Bayesian Network

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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(6) Bayesian Networks: P(C=T) P(C=F) 0,5 0,5 Cloudy C P(R=T) P(R=F) 0,8 0,2 0,2 0,8 F Sprinkler Rain c P(S=T) P(S=F) 0,1 0,5 0,9 0,5 F WetGrass P(W=T) P(W=F) 0,01 0,1 0,1 1,0 R 0,99 F 0,9 0,9 F T F F 0,0 (a) Given the above Bayesian network, compute the probability: P(Wetgrass = %3D F| Sprinkler = F). Show the steps. (b) Given the above Bayesian network, compute the probability P(Rain = T| sprinkler = T) (c) Write the full Joint probability distribution (as a multiplication of conditional probabilities), for both the above Bayesian Network, as well as the network after we reverse the arrows. That is, how would you compute P(cloudy , sprinkler, rain , wetgrass) given the conditional probability tables of the Bayesian network (also do the question with the arrows reversed)
Transcribed Image Text:(6) Bayesian Networks: P(C=T) P(C=F) 0,5 0,5 Cloudy C P(R=T) P(R=F) 0,8 0,2 0,2 0,8 F Sprinkler Rain c P(S=T) P(S=F) 0,1 0,5 0,9 0,5 F WetGrass P(W=T) P(W=F) 0,01 0,1 0,1 1,0 R 0,99 F 0,9 0,9 F T F F 0,0 (a) Given the above Bayesian network, compute the probability: P(Wetgrass = %3D F| Sprinkler = F). Show the steps. (b) Given the above Bayesian network, compute the probability P(Rain = T| sprinkler = T) (c) Write the full Joint probability distribution (as a multiplication of conditional probabilities), for both the above Bayesian Network, as well as the network after we reverse the arrows. That is, how would you compute P(cloudy , sprinkler, rain , wetgrass) given the conditional probability tables of the Bayesian network (also do the question with the arrows reversed)
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