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The normal distribution (Gauss) in 1D
(
)
2
2
0
(
)
2
0
0
e
Pr
, ,
d
2
1
CDF 1 Erf
2
2
x
x
X x
x
x
µ
σ
µ σ
πσ
µ
σ
−
−
−∞
≤
=
=
−
= = +
∫
Probability Density Function, PDF
Cumulative Density Function, CDF
[
]
(
)
2
2
(
)
2
Pr
,
d , ,
e
PDF d
d
2
x
X x x x
x
x
µ
σ
µ σ
πσ
−
−
∈ +
=
= ⋅
=
( )
( )
PDF d 1
CDF 1
x x
∞
−∞
⋅
≡
∞ ≡
∫
Normalization requirements: