Introduction to turbulence/Statistical analysis/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
Gaussian (or normal) distributions