Dose 2016

Rotational symmetrical 3D Gauss – cumulative function

Probability that we find something within a sphere of radius R :

2

r

2

2

−

R ∫

  

  

R

Σ

2

2

e

2

Σ

R

Σ

Σ ≤ =

⋅

[ ] = =

−

⋅

⋅

−

2

(

)

2

Pr

,

4 d ... r r π

Erf

e

r R

R

Σ

3

π

2

3

( ) 2

2 π Σ

0

0.90

Note:

(

)

Pr

,

0.90

2.5001

r R

Σ ≤ =

R

Σ

⇒

=

⋅

2.5

The probability that a sphere of radius R is completely contained within R+2.5 . Σ is 90%!