Lecture 8: Gaussian Distribution

Physics 3719Spring Semester 2011

Carl Friedrich Gauss(1777-1855) on the

German 10 Mark Note

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Binomial Distribution

Poisson Distribution

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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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What Happens as Becomes Large?

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What Happens as Becomes Large?

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What Happens as Becomes Large?

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What Happens as Becomes Large?

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What Happens as Becomes Large?

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What Happens as Becomes Large?

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What Happens as Becomes Large?

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What Happens as Becomes Large?

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What Happens as Becomes Large?

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What Happens as Becomes Large?

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What Happens as Becomes Large?

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Binomial Distribution

Poisson Distribution

Gaussian (Normal)Distribution

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Properties of the Gaussian Distribution

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Gaussian Distribution

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Gaussian Distribution

A “1 sigma” error interval is not all-inclusive!

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Use “2/3” Rule as a Rough Guide

● Spread of points, error bars consistent with normal error distribution.

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Use “2/3” Rule as a Rough Guide

● What is the problem here?

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Use “2/3” Rule as a Rough Guide

● What is the problem here?

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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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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