EasyManuals Logo

Mirion Technologies GEM-5 User Manual

Default Icon
443 pages
To Next Page IconTo Next Page
To Next Page IconTo Next Page
To Previous Page IconTo Previous Page
To Previous Page IconTo Previous Page
Page #287 background imageLoading...
Page #287 background image
Counting Statistics
Gem-5 User’s Manual 271
The standard deviation can be calculated by solving the following integral:
Equation 9 Standard Deviation of Normal Distribution
∫
+∞
∞−
−= dx)x(G)x(
22
µσ
(9)
The probability for
x
to fall between
1
x
and
2
x
is defined by the following integral:
Equation 10 Probability of x to Fall Between x
1
and x
2
( )
∫
−
−
=<<
2
1
2
2
x
x
2
x
21
dxe
2
1
)xxx(P
σ
µ
σπ
(10)
With
σµ
−=
1
x
and
σµ
+=
2
x
the integral from Equation 10 is known as two
tailed Gaussian integral and gives the probability that a point lies within the given
number of σ from the mean μ.
An individual observation from a normal distribution has a probability of 68% of
falling within ±1σ of mean, 95% of falling within ±2σ of mean and 99.7% of falling
within ±3σ of mean.
Equation 11 Two-Tailed Probability
( )
∫
+
−
−
−
−
=+<<−
σµ
σµ
σ
µ
σπ
σµσµ
dxe
2
1
)x(P
2
2
2
x
tailed2
(11)
Figure 128: Two-tailed distribution
In a special case when
0=
µ
and using the substituition
2
x
t
σ
=
in Equation 11, the two-
tailed probability can be written in the following form:

Table of Contents

Questions and Answers:

Question and Answer IconNeed help?

Do you have a question about the Mirion Technologies GEM-5 and is the answer not in the manual?

Mirion Technologies GEM-5 Specifications

General IconGeneral
BrandMirion Technologies
ModelGEM-5
CategoryMonitor
LanguageEnglish

Related product manuals