# Introduction to turbulence/Statistical analysis/Probability

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=== The histogram and probability density function === | === The histogram and probability density function === | ||

- | The frequency of occurence of a given ''amplitude'' (or value) from a finite number of realizations of a random variable can be displayed by dividing the range of possible values of the random variables into a number of slots (or windows). | + | The frequency of occurence of a given ''amplitude'' (or value) from a finite number of realizations of a random variable can be displayed by dividing the range of possible values of the random variables into a number of slots (or windows). Since all possible values are covered, each realization fits into only one window. For every realization a count is entered into the appropriate window. When all the realizations have been considered, the number of counts in each window is divided by the total number of realizations. The result is called the '''histogram''' (or ''frequency of occurendce'' diagram). From the definitioin it follows immediately that the sum of the values of all the windows is exactly one. |

+ | |||

+ | The shape of a | ||

=== The probability distribution === | === The probability distribution === |

## Revision as of 09:09, 29 May 2006

## Contents |

## Probability

### The histogram and probability density function

The frequency of occurence of a given *amplitude* (or value) from a finite number of realizations of a random variable can be displayed by dividing the range of possible values of the random variables into a number of slots (or windows). Since all possible values are covered, each realization fits into only one window. For every realization a count is entered into the appropriate window. When all the realizations have been considered, the number of counts in each window is divided by the total number of realizations. The result is called the **histogram** (or *frequency of occurendce* diagram). From the definitioin it follows immediately that the sum of the values of all the windows is exactly one.

The shape of a

### The probability distribution

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### Gaussian (or normal) distributions

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