Dose 2016

The normal distribution (Gauss) in 1D

Cumulative Density Function, CDF

Probability Density Function, PDF

2

(

)

−

µ

x

−

2

x

0

2

(

)

e

[

]

σ

Pr

,

d , ,

X x x x ∈ +

∫

≤

=

=

=

(

)

µ σ

Pr

, ,

d

X x

x

µ σ

0

2

πσ

2

−∞

(

)

x

µ

−



 −  

−

2

1 CDF 1 Erf 2

x

2

e

σ

µ

= = +

0

 

 

 

PDF d

d

x

x

= ⋅

=



2

2

σ

πσ

∞ ∫

( )

PDF d 1 x x ⋅ ≡

Normalization requirements:

−∞

( )

CDF 1 ∞ ≡