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Cumulative Distribution Function - Probability

Published: 2012/02/11

Channel: Engineer Clearly

The Probability Distribution Function (PDF) of [X]

Published: 2014/02/26

Channel: MIT OpenCourseWare

Probability density functions | Probability and Statistics | Khan Academy

Published: 2009/02/16

Channel: Khan Academy

Constructing a probability distribution for random variable | Khan Academy

Published: 2014/02/07

Channel: Khan Academy

Calculating a Cumulative Distribution Function (CDF)

Published: 2014/02/26

Channel: MIT OpenCourseWare

Probability Mass Function & Density Function in Hindi

Published: 2015/05/15

Channel: Bhagwan Singh Vishwakarma

Continuous Random Variables: Cumulative Distribution Functions

Published: 2012/11/27

Channel: MrNichollTV

Cumulative Distribution Function : Example : ExamSolutions

Published: 2009/12/05

Channel: ExamSolutions

Probability Density Functions / Continuous Random Variables

Published: 2009/06/26

Channel: patrickJMT

Binomial CDF (Cumulative Distribution Function) on TI-83 & TI-84

Published: 2015/08/23

Channel: OpenIntroOrg

The Amazing Normal Distribution Function

Published: 2006/09/09

Channel: k0x

Cumulative distribution function technique

Published: 2016/03/10

Channel: Lawrence Leemis

Gaussian

Published: 2012/12/12

Channel: Paul Francis

Cumulative Distribution Function

Published: 2012/06/13

Channel: David Waldo

Probability : Cumulative Distribution Function F(X) : ExamSolutions

Published: 2011/04/14

Channel: ExamSolutions

Section 5 1 Distribution Function Technique

Published: 2017/04/19

Channel: Karen Benway

probability density functions and cumulative distribution functions s1

Published: 2013/02/14

Channel: Rhys Steele

Cumulative Distribution Functions : Introduction : ExamSolutions

Published: 2009/12/04

Channel: ExamSolutions

Finding a CDF from a pdf

Published: 2015/11/26

Channel: Mr Camilleri

PDF and CDF Explanations

Published: 2011/04/21

Channel: UAMath115

Discrete Random Variables 1) Brief Intro Probability Distribution and Function

Published: 2013/08/26

Channel: ukmathsteacher

Method of Distribution Functions 1

Published: 2014/11/03

Channel: Matthew Jones

Mod-01 Lec-16 CUMULATIVE DISTRIBUTION FUNCTION

Published: 2015/02/19

Channel: nptelhrd

Introduction to discrete probability distributions

Published: 2012/12/07

Channel: Khan Academy

Discrete Random Variables 2) Cumulative Distribution Function

Published: 2013/08/26

Channel: ukmathsteacher

Lecture - 5 Probability Distributions and Density Functions

Published: 2008/07/10

Channel: nptelhrd

Optics 2: Validity of Wigner Distribution Function for Ray-based Imaging

Published: 2011/04/13

Channel: cmurobotics

Orbitals: Nodes and Radial Distribution Function

Published: 2017/02/25

Channel: Chemistry_OK OSU

Cumulative Distribution Function of an Order Statistic

Published: 2014/10/06

Channel: Ben Garside

Uniform distribution cumulative distribution function

Published: 2016/02/12

Channel: Lawrence Leemis

Features of the Fermi Dirac Distribution Function

Published: 2011/09/20

Channel: nptelhrd

The Binomial Distribution / Binomial Probability Function

Published: 2009/05/06

Channel: patrickJMT

Python tutorial: Cumulative Distribution Functions

Published: 2016/11/09

Channel: DataCamp

Properties of the probability distribution function

Published: 2014/11/03

Channel: Jochumzen

Normal distribution's probability density function derived in 5min

Published: 2013/08/22

Channel: acadelivery

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

Published: 2013/12/24

Channel: Michel van Biezen

Prob 3 2 Properties of Distribution Function

Published: 2014/01/19

Channel: Quant Education

Cumulative Distribution Function for C.R.V | دالة التوزيع التراكمية لمتغير عشوائي متصل

Published: 2016/12/27

Channel: jamal505

Geometric distribution cumulative distribution function

Published: 2016/02/02

Channel: Lawrence Leemis

Bidirectional Reflectance Distribution Function

Published: 2012/09/24

Channel: UCDavis

Distribution Function in R

Published: 2016/08/17

Channel: vivek belhekar

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

Published: 2011/01/05

Channel: stepbil

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

Published: 2016/12/24

Channel: jamal505

Cumulative distribution function introduction

Published: 2012/11/02

Channel: learnittcom

Probability Basics II: The Cumulative Distribution Function (cdf), 2/3/2015

Published: 2015/03/03

Channel: Lutfi Al-Sharif The University of Jordan

Calculating Probabilities Using the Normal Distribution Function in Excel

Published: 2015/02/28

Channel: Todd Grande

virtuallymath.com: how to write a cumulative probability distribution function

Published: 2013/06/10

Channel: calculuscoaches

Hydrogen Atom Radial Probability Distribution for 2s And 3s Orbital

Published: 2013/09/01

Channel: Patterns Remonstrator

Atom Electron Orbitals and Radial Distribution Function

Published: 2015/05/12

Channel: NinetyEast

Lecture 09 - Continuous distribution functions and empirical distribution functions

Published: 2017/07/30

Channel: Modeling and Simulation of Discrete Event Systems

This article
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*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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