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Bayesian Networks
book

Bayesian Networks

by Marco Scutari, Jean-Baptiste Denis
June 2014
Intermediate to advanced content levelIntermediate to advanced
241 pages
6h 20m
English
CRC Press
Content preview from Bayesian Networks
Solutions 205
To simplify the notation, we will first transform the three variables to give
them a zero marginal expectation and a unity marginal variance.
e
G =
G E(G)
p
VAR(G)
=
G 50
10
e
E =
E E(E)
p
VAR(E)
=
E 50
10
e
V =
V E(V)
p
VAR(V)
=
V 50
10
The resulting normalised variables are
e
G N (0, 1) ,
e
E N (0, 1) ,
e
V |
e
G,
e
E N
1
2
e
G +
r
1
2
e
E,
1
2
2
!
.
We are now able to compute the joint density of the three transformed vari-
ables
f
e
G = g,
e
E = e,
e
V = v
f
e
G = g
+ f
e
E = e
+ f
e
V = v |
e
G = g,
e
E = e
=
g
2
2
e
2
2
2
v
1
2
g
r
1
2
e
!
2
=
g
e
v
T
1
2
2
1
2
2
3
2
2
1
2 2
g
e
v
=
1
2
g
e
v
T
1 0
1
2
0 1
q
1
2
1
2
q
1
2
1
1
g
e
v
.
Now
VAR
e
G
e
E
e
V
=
1 0
1
2
0 1
q
1
2
1
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Publisher Resources

ISBN: 9781482225587