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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 74EQ

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A Bayesian network is represented in the graph below with each variable to be binary. There are 8 observations as listed in the table
below. Now please estimate P(A=1) and P(E=1|B=1,C=1).
A
1
1
0
0
0
0
D
1
1
1
0
1
1
B
A B
10
00 1
1
0
1
0
1
0
F
E
C
C
D
E
1 0 1
1
1
0
0
1
0
0
F
1
01
0
1
0 0
1 0
1 0
1
1
0
0
Select one:
A. P(A-1)=3/8, P(E=1|B=1,C=1)=2/3
B. P(A-1)=3/8, P(E=1|B=1,C=1)=1/2
C. P(A-1)=5/8, P(E=1|B=1,C=1)=2/3
D. P(A-1)=5/8, P(E=1|B=1,C=1)=1/2

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