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Cumulative Distribution Function - Probability

Published: 2012/02/11

Channel: Engineer Clearly

Probability density functions | Probability and Statistics | Khan Academy

Published: 2009/02/16

Channel: Khan Academy

The Probability Distribution Function (PDF) of [X]

Published: 2014/02/26

Channel: MIT OpenCourseWare

Calculating a Cumulative Distribution Function (CDF)

Published: 2014/02/26

Channel: MIT OpenCourseWare

Constructing a probability distribution for random variable | Khan Academy

Published: 2014/02/07

Channel: Khan Academy

Probability Mass Function & Density Function in Hindi

Published: 2015/05/15

Channel: Bhagwan Singh Vishwakarma

probability density functions and cumulative distribution functions s1

Published: 2013/02/14

Channel: Rhys Steele

Probability Density Functions / Continuous Random Variables

Published: 2009/06/26

Channel: patrickJMT

PDF and CDF Explanations

Published: 2011/04/21

Channel: UAMath115

Probability : Cumulative Distribution Function F(X) : ExamSolutions

Published: 2011/04/14

Channel: ExamSolutions

Orbitals: Nodes and Radial Distribution Function

Published: 2017/02/25

Channel: Chemistry_OK OSU

Continuous Random Variables: Cumulative Distribution Functions

Published: 2012/11/27

Channel: MrNichollTV

Finding a CDF from a pdf

Published: 2015/11/26

Channel: Mr Camilleri

Method of Distribution Functions 1

Published: 2014/11/03

Channel: Matthew Jones

Cumulative Distribution Function

Published: 2012/06/13

Channel: David Waldo

Continuous Random Variables: Probability Density Functions

Published: 2014/01/28

Channel: MrNichollTV

Lecture - 5 Probability Distributions and Density Functions

Published: 2008/07/10

Channel: nptelhrd

Cumulative Distribution Function : Example : ExamSolutions

Published: 2009/12/05

Channel: ExamSolutions

Cumulative Distribution Functions : Introduction : ExamSolutions

Published: 2009/12/04

Channel: ExamSolutions

Mod-01 Lec-16 CUMULATIVE DISTRIBUTION FUNCTION

Published: 2015/02/19

Channel: nptelhrd

Section 5 1 Distribution Function Technique

Published: 2017/04/19

Channel: Karen Benway

Discrete Random Variables 1) Brief Intro Probability Distribution and Function

Published: 2013/08/26

Channel: ukmathsteacher

Discrete Random Variables 2) Cumulative Distribution Function

Published: 2013/08/26

Channel: ukmathsteacher

An Introduction to the Normal Distribution

Published: 2012/12/23

Channel: jbstatistics

Prob 3 2 Properties of Distribution Function

Published: 2014/01/19

Channel: Quant Education

Python tutorial: Cumulative Distribution Functions

Published: 2016/11/09

Channel: DataCamp

PDF #1 (Deriving Cumulative Distribution Function from Probability Density Function)

Published: 2011/01/05

Channel: stepbil

An Introduction to Continuous Probability Distributions

Published: 2012/12/23

Channel: jbstatistics

Introduction to discrete probability distributions

Published: 2012/12/07

Channel: Khan Academy

Gaussian

Published: 2012/12/12

Channel: Paul Francis

Chemistry - Electron Structures in Atoms (26 of 40) Radial Probability Density Function: S-Orbital

Published: 2013/12/24

Channel: Michel van Biezen

Marginal distribution and conditional distribution

Published: 2016/11/16

Channel: Khan Academy

Normal distribution's probability density function derived in 5min

Published: 2013/08/22

Channel: acadelivery

FRM: Normal probability distribution

Published: 2008/01/15

Channel: Bionic Turtle

Cumulative Distribution Function for D.R.v|دالة التوزيع التراكمية لمتغير عشوائي منفصل

Published: 2016/12/24

Channel: jamal505

Exponential distribution cumulative distribution function

Published: 2016/02/16

Channel: Lawrence Leemis

Electronic Devices: Fermi Dirac distribution

Published: 2015/05/04

Channel: techgurukula

The Binomial Distribution / Binomial Probability Function

Published: 2009/05/06

Channel: patrickJMT

Joint Probability Distribution # 1 | Marginal Distributions & Expected Values

Published: 2015/02/24

Channel: WelshBeastMaths

Probability Mass Function

Published: 2012/02/11

Channel: Engineer Clearly

Cumulative distribution function introduction

Published: 2012/11/02

Channel: learnittcom

An Introduction to the Continuous Uniform Distribution

Published: 2012/12/28

Channel: jbstatistics

39- Joint CDF

Published: 2015/03/26

Channel: Probability Course

Continuous probability distribution intro

Published: 2012/12/10

Channel: Khan Academy

Finding Probabilities and Percentiles for a Continuous Probability Distribution

Published: 2012/12/28

Channel: jbstatistics

Multivariate distributions: joint cumulative distribution functions -- Example 1

Published: 2016/03/09

Channel: Lawrence Leemis

The Amazing Normal Distribution Function

Published: 2006/09/09

Channel: k0x

Cumulative distribution function technique

Published: 2016/03/10

Channel: Lawrence Leemis

Cumulative Distribution Function of an Order Statistic

Published: 2014/10/06

Channel: Ben Garside

How to Construct a Cumulative Distribution Plot in Excel 2007

Published: 2011/10/18

Channel: Dr. Cyders

This article does not cite any sources. (December 2009) (Learn how and when to remove this template message) |

*This article describes the*distribution function*as used in physics. You may be looking for the related mathematical concepts of cumulative distribution function or probability density function.*

In molecular kinetic theory in physics, a particle's **distribution function** is a function of seven variables, , which gives the number of particles per unit volume in single-particle phase space. It is the number of particles per unit volume having approximately the velocity near the place and time . The usual normalization of the distribution function is

where, *N* is the total number of particles, and *n* is the number density of particles – the number of particles per unit volume, or the density divided by the mass of individual particles.

A distribution function may be specialised with respect to a particular set of dimensions. E.g. take the quantum mechanical six-dimensional phase space, and multiply by the total space volume, to give the momentum distribution, i.e. the number of particles in the momentum phase space having approximately the momentum .

Particle distribution functions are often used in plasma physics to describe wave–particle interactions and velocity-space instabilities. Distribution functions are also used in fluid mechanics, statistical mechanics and nuclear physics.

The basic distribution function uses the Boltzmann constant and temperature with the number density to modify the normal distribution:

Related distribution functions may allow bulk fluid flow, in which case the velocity origin is shifted, so that the exponent's numerator is , where is the bulk velocity of the fluid. Distribution functions may also feature non-isotropic temperatures, in which each term in the exponent is divided by a different temperature.

Plasma theories such as magnetohydrodynamics may assume the particles to be in thermodynamic equilibrium. In this case, the distribution function is *Maxwellian*. This distribution function allows fluid flow and different temperatures in the directions parallel to, and perpendicular to, the local magnetic field. More complex distribution functions may also be used, since plasmas are rarely in thermal equilibrium.

The mathematical analog of a distribution is a measure; the time evolution of a measure on a phase space is the topic of study in dynamical systems.

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