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Lecture 8: Gaussian Distribution
Physics 3719Spring Semester 2011
Carl Friedrich Gauss(1777-1855) on the
German 10 Mark Note
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7 February 2011 Physics 3719 Lecture 8 2
Binomial Distribution
Poisson Distribution
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7 February 2011 Physics 3719 Lecture 8 3
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7 February 2011 Physics 3719 Lecture 8 4
Example of Poisson Distribution
● Poisson distributed data can take on discrete integer values.
● n must be an integer
● need not be!
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7 February 2011 Physics 3719 Lecture 8 5
What Happens as Becomes Large?
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7 February 2011 Physics 3719 Lecture 8 6
What Happens as Becomes Large?
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7 February 2011 Physics 3719 Lecture 8 7
What Happens as Becomes Large?
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7 February 2011 Physics 3719 Lecture 8 8
What Happens as Becomes Large?
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7 February 2011 Physics 3719 Lecture 8 9
What Happens as Becomes Large?
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7 February 2011 Physics 3719 Lecture 8 10
What Happens as Becomes Large?
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7 February 2011 Physics 3719 Lecture 8 11
What Happens as Becomes Large?
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7 February 2011 Physics 3719 Lecture 8 12
What Happens as Becomes Large?
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7 February 2011 Physics 3719 Lecture 8 13
What Happens as Becomes Large?
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7 February 2011 Physics 3719 Lecture 8 14
What Happens as Becomes Large?
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7 February 2011 Physics 3719 Lecture 8 15
What Happens as Becomes Large?
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7 February 2011 Physics 3719 Lecture 8 16
Binomial Distribution
Poisson Distribution
Gaussian (Normal)Distribution
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7 February 2011 Physics 3719 Lecture 8 17
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7 February 2011 Physics 3719 Lecture 8 18
Properties of the Gaussian Distribution
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7 February 2011 Physics 3719 Lecture 8 19
Gaussian Distribution
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7 February 2011 Physics 3719 Lecture 8 20
Gaussian Distribution
A “1 sigma” error interval is not all-inclusive!
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7 February 2011 Physics 3719 Lecture 8 21
Use “2/3” Rule as a Rough Guide
● Spread of points, error bars consistent with normal error distribution.
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7 February 2011 Physics 3719 Lecture 8 22
Use “2/3” Rule as a Rough Guide
● What is the problem here?
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7 February 2011 Physics 3719 Lecture 8 23
Use “2/3” Rule as a Rough Guide
● What is the problem here?
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7 February 2011 Physics 3719 Lecture 8 24
2 Tests● In situations where uncertainties are (or are
approximately) Gaussian, one often tests the goodness of the model by performing a 2 test.
● Lab 2:
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7 February 2011 Physics 3719 Lecture 8 25
Additional Reading and Problems
● Read in Taylor: – Ch 5: The Normal
Distribution (Sections 1 and 2)
– Chapter 10: The Binomial Distribution
– Ch 11: The Poisson Distribution
● Try the problems:– 5.4, 5.6, 5.12– 10.9, 10.10, 10.11,
10.20, 10.21, 10.22– 11.1, 11.3, 11.8,
11.10, 11.14, 11.18, 11.20