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Z - Old
Probalistc Models
Math - part 1
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Part_01_introduction
A)
1.0
B)
2x2x2x2x4
2
P(x) represents the system's
degree
of
belief
Joint and Marginal Distributions
A)
0.15+0.1+0.1+0.03
B)
0.03+0.04+0.05+0.5
C)
0.62,0.38
3
Joint and Marginal Distributions (2)
A)
0.1+0.03+0.05+0.5
B)
0.15+0.03+0.1
+0.05
1
P
(
α
∩
β
)
P(\alpha \cap \beta)
P
(
α
∩
β
)
=
P
(
α
∣
β
)
P(\alpha | \beta)
P
(
α
∣
β
)
P
(
β
)
P(\beta)
P
(
β
)
P
(
α
∩
β
)
P(\alpha \cap \beta)
P
(
α
∩
β
)
=
P
(
β
∩
α
)
P(\beta \cap \alpha )
P
(
β
∩
α
)
Chain Rule for Probability
A)
4,3,2,1
B)
3,2,1
C)
2,1
D)
1
4
Law of total probability
P
(
x
)
P(x)
P
(
x
)
=
∑
y
∈
V
a
l
(
y
)
\sum_{y \in Val(y)}
∑
y
∈
Va
l
(
y
)
P
(
x
,
y
)
P(x,y)
P
(
x
,
y
)
A)
x|y
B)
y
C)
x
D)
y|x
4
Marginal
distributions :
P
(
X
)
=
P(X) =
P
(
X
)
=
∑
y
P
(
X
,
y
)
\sum_y P(X,y)
∑
y
P
(
X
,
y
)
Conditional
distributions :
P
(
X
∣
Z
)
P(X|Z)
P
(
X
∣
Z
)
=
∑
y
P
(
X
,
y
∣
Z
)
\sum_y P(X,y | Z)
∑
y
P
(
X
,
y
∣
Z
)
P
(
α
∣
β
)
P(\alpha | \beta)
P
(
α
∣
β
)
=
P
(
β
∣
α
)
P
(
α
)
P(\beta | \alpha) P(\alpha)
P
(
β
∣
α
)
P
(
α
)
/
P
(
β
)
P(\beta)
P
(
β
)
Inference by enumeration :
A)
0.1+0.03+0.04+0.5
B)
0.1+0.05
2
Inference by enumeration (2)
A)
0.1+0.03
B)
0.1+0.03+0.04+0.5
2
Inference by enumeration (3)
A)
0.1+0.03
B)
0.04+0.5
2
The general inference-by-Enumeration Algorithm
A)
0.1+0.03
B)
0.04+0.5
C)
0.13+0.54
D)
Z
4
Test Yourself
A)
0.5, 0.5
B)
0.4, 0.6
C)
0.75, 0.33
D)
0.25, 0.67
E)
0.6, 0.4
F)
0.2, 0.8
6
Joint vs Posterior
A)
0.2,0.4
B)
0.33,0.67
2
to do
55
/
65
part
2
fundamentals
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