(6) Bayesian Networks:P(C=T) P(C=F)0,50,5CloudyC P(R=T) P(R=F)0,80,20,20,8FSprinklerRainc P(S=T) P(S=F)0,10,50,90,5FWetGrassP(W=T) P(W=F)0,010,10,11,0R0,99F0,90,9F TFF0,0(a) Given the above Bayesian network,compute the probability: P(Wetgrass =%3DF| Sprinkler = F). Show the steps.(b) Given the above Bayesian network,compute the probability P(Rain = T|sprinkler = T)(c) Write the full Joint probabilitydistribution (as a multiplication ofconditional probabilities), for both theabove Bayesian Network, as well as thenetwork after we reverse the arrows.That is, how would you compute P(cloudy ,sprinkler, rain , wetgrass) given theconditional probability tables of theBayesian network (also do the question withthe arrows reversed)

Answered: Bayesian Network

Engineering

Computer Science

Bayesian Network

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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Question

(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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