In statistical mechanics, the radial distribution function, (or pair correlation function) in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle.
If a given particle is taken to be at the origin O, and if is the average number density of particles, then the local time-averaged density at a distance from O is . This simplified definition holds for a homogeneous and isotropic system. A more general case will be considered below.
In simplest terms it is a measure of the probability of finding a particle at a distance of away from a given reference particle, relative to that for an ideal gas. The general algorithm involves determining how many particles are within a distance of r and r+dr away from a particle. This general theme is depicted to the right, where the red particle is our reference particle, and blue particles are those which are within the circular shell, dotted in orange.
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
Here, 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 .
Probability Distribution Functions (PMF, PDF, CDF)
See all my videos at http://www.zstatistics.com/videos
0:00 Intro
0:43 Terminology defined
DISCRETE VARIABLE:
2:24 Probability Mass Function (PMF)
3:31 Cumulative Distribution Function (CDF) - discrete
CONTINUOUS VARIABLE:
7:00 Probability Density Function (PDF)
8:54 Cumulative Distribution Function (CDF) - continuous
published: 02 Mar 2020
Cumulative Distribution Functions and Probability Density Functions
This statistics video tutorial provides a basic introduction into cumulative distribution functions and probability density functions. The probability density function or pdf is f(x) which describes the shape of the distribution. It can tell you if you have a uniform, exponential, or normal distribution. The cumulative distribution function or cdf allows you to calculate the area under the curve to the left of some point of interest in order to evaluate the accumulated probability.
Probability Formula Sheet:
https://bit.ly/3zb22rW
Introduction to Probability:
https://www.youtube.com/watch?v=SkidyDQuupA
Probability Formulas:
https://www.youtube.com/watch?v=bddckR734aM
Probability Explained: ...
published: 21 Sep 2019
Distribution Function Technique to Find The Probability Density Function of a New Random Variable
published: 03 Jul 2022
L08.7 Cumulative Distribution Functions
MIT RES.6-012 Introduction to Probability, Spring 2018
View the complete course: https://ocw.mit.edu/RES-6-012S18
Instructor: John Tsitsiklis
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
published: 24 Apr 2018
Calculating a Cumulative Distribution Function (CDF)
MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
View the complete course: http://ocw.mit.edu/6-041SCF13
Instructor: Jimmy Li
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
published: 26 Feb 2014
To find CDF when PDF of continuous random variable is given
see short method to find cdf in following video
https://www.youtube.com/watch?v=qmzfbuTeCRw
published: 16 Mar 2023
Constructing a probability distribution for random variable | Khan Academy
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/e/constructing-probability-distributions?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Watch the next lesson: https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/v/probability-density-functions?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Missed the previous lesson?
https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/v/discrete-and-continuous-random-variables?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Probability and statistics on Khan Academy: We dare you to go through a day in ...
published: 07 Feb 2014
02 - Random Variables and Discrete Probability Distributions
Get more lessons & courses at http://www.mathtutordvd.com
In this lesson, the student will learn the concept of a random variable in statistics. We will then use the idea of a random variable to describe the discrete probability distribution, which is a key idea used to solve statistics problems.
published: 08 Sep 2017
Distribution function examples ch 12 lec 14
Random numbers are numbers obtained by some random process. Random variables are called stochastic variable and chance variable. Experiment is a process which generates raw data. Experiment in which outcomes vary from trial to trial are called random experiments. A variable whose value are determined by outcomes of a random experiment are called random variable.
I am here to teach you the most important subject of your course that is statistics. I hope you will love to my content and i am hopeful and try to present myself in front of you.
Youtube channal https://www.youtube.com/channel/UCcvn...
Face book page https://web.facebook.com/Nazz-Academy...
Instagram https://www.instagram.com/nazzacademy11
published: 29 Jul 2021
Probability Density Functions
This calculus 2 video tutorial provides a basic introduction into probability density functions. It explains how to find the probability that a continuous random variable such as x in somewhere between two values by evaluating the definite integral from a to b. The probability is equivalent to the area under the curve. This video also contains an example problem with an exponential density function involving the mean u which represents the average wait time for a customer in the example problem.
Improper Integrals:
https://www.youtube.com/watch?v=ND9cEdfCFr0
Integration Into Inverse Trig:
https://www.youtube.com/watch?v=AE-0gXXx_j0
Integration of Rational Functions:
https://www.youtube.com/watch?v=4yJmhZBB40w
Integral o...
See all my videos at http://www.zstatistics.com/videos
0:00 Intro
0:43 Terminology defined
DISCRETE VARIABLE:
2:24 Probability Mass Function (PMF)
3:31 Cumula...
See all my videos at http://www.zstatistics.com/videos
0:00 Intro
0:43 Terminology defined
DISCRETE VARIABLE:
2:24 Probability Mass Function (PMF)
3:31 Cumulative Distribution Function (CDF) - discrete
CONTINUOUS VARIABLE:
7:00 Probability Density Function (PDF)
8:54 Cumulative Distribution Function (CDF) - continuous
See all my videos at http://www.zstatistics.com/videos
0:00 Intro
0:43 Terminology defined
DISCRETE VARIABLE:
2:24 Probability Mass Function (PMF)
3:31 Cumulative Distribution Function (CDF) - discrete
CONTINUOUS VARIABLE:
7:00 Probability Density Function (PDF)
8:54 Cumulative Distribution Function (CDF) - continuous
This statistics video tutorial provides a basic introduction into cumulative distribution functions and probability density functions. The probability density ...
This statistics video tutorial provides a basic introduction into cumulative distribution functions and probability density functions. The probability density function or pdf is f(x) which describes the shape of the distribution. It can tell you if you have a uniform, exponential, or normal distribution. The cumulative distribution function or cdf allows you to calculate the area under the curve to the left of some point of interest in order to evaluate the accumulated probability.
Probability Formula Sheet:
https://bit.ly/3zb22rW
Introduction to Probability:
https://www.youtube.com/watch?v=SkidyDQuupA
Probability Formulas:
https://www.youtube.com/watch?v=bddckR734aM
Probability Explained:
https://www.youtube.com/watch?v=UORztmWGY6Q
Probability With Geometry:
https://www.youtube.com/watch?v=DeH5aHWxEaI
Probability of Complementary Events:
https://www.youtube.com/watch?v=0T-CaQCiSf4
Conditional Probability:
https://www.youtube.com/watch?v=sqDVrXq_eh0
__________________________________
Independent and Dependent Events:
https://www.youtube.com/watch?v=lWAdPyvm400
Probability of Mutual Exclusive Events:
https://www.youtube.com/watch?v=X6usGgwXFyU
Multiplication and Addition Rule:
https://www.youtube.com/watch?v=94AmzeR9n2w
Compound Probability:
https://www.youtube.com/watch?v=EHU6pVSczb4
Expected Value:
https://www.youtube.com/watch?v=b6VK2VPMXNI
Probability Tree Diagrams:
https://www.youtube.com/watch?v=w4wKXVwtGac
___________________________________
Bayes Theorem:
https://www.youtube.com/watch?v=OByl4RJxnKA
Probability - Binomial Distribution:
https://www.youtube.com/watch?v=3PWKQiLK41M
Probability - Geometric Distribution:
https://www.youtube.com/watch?v=d5iAWPnrH6w
Probability - Poisson Distribution:
https://www.youtube.com/watch?v=m0o-585xwW0
Continuous Probability Distributions:
https://www.youtube.com/watch?v=QxqxdQ_g2uw
Probability Density Functions:
https://www.youtube.com/watch?v=3xAIWiTJCvE
__________________________________
Probability - Uniform Distributions:
https://www.youtube.com/watch?v=KfunVw-0AH0
Probability - Exponential Distributions:
https://www.youtube.com/watch?v=J3KSjZFVbis
Probability - Normal Distributions (Calculus):
https://www.youtube.com/watch?v=gHBL5Zau3NE
Probability - Standard Normal Distributions:
https://www.youtube.com/watch?v=CjF_yQ2N638
Probability - The Law of Large Numbers:
https://www.youtube.com/watch?v=ihTpK6dXSas
___________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
This statistics video tutorial provides a basic introduction into cumulative distribution functions and probability density functions. The probability density function or pdf is f(x) which describes the shape of the distribution. It can tell you if you have a uniform, exponential, or normal distribution. The cumulative distribution function or cdf allows you to calculate the area under the curve to the left of some point of interest in order to evaluate the accumulated probability.
Probability Formula Sheet:
https://bit.ly/3zb22rW
Introduction to Probability:
https://www.youtube.com/watch?v=SkidyDQuupA
Probability Formulas:
https://www.youtube.com/watch?v=bddckR734aM
Probability Explained:
https://www.youtube.com/watch?v=UORztmWGY6Q
Probability With Geometry:
https://www.youtube.com/watch?v=DeH5aHWxEaI
Probability of Complementary Events:
https://www.youtube.com/watch?v=0T-CaQCiSf4
Conditional Probability:
https://www.youtube.com/watch?v=sqDVrXq_eh0
__________________________________
Independent and Dependent Events:
https://www.youtube.com/watch?v=lWAdPyvm400
Probability of Mutual Exclusive Events:
https://www.youtube.com/watch?v=X6usGgwXFyU
Multiplication and Addition Rule:
https://www.youtube.com/watch?v=94AmzeR9n2w
Compound Probability:
https://www.youtube.com/watch?v=EHU6pVSczb4
Expected Value:
https://www.youtube.com/watch?v=b6VK2VPMXNI
Probability Tree Diagrams:
https://www.youtube.com/watch?v=w4wKXVwtGac
___________________________________
Bayes Theorem:
https://www.youtube.com/watch?v=OByl4RJxnKA
Probability - Binomial Distribution:
https://www.youtube.com/watch?v=3PWKQiLK41M
Probability - Geometric Distribution:
https://www.youtube.com/watch?v=d5iAWPnrH6w
Probability - Poisson Distribution:
https://www.youtube.com/watch?v=m0o-585xwW0
Continuous Probability Distributions:
https://www.youtube.com/watch?v=QxqxdQ_g2uw
Probability Density Functions:
https://www.youtube.com/watch?v=3xAIWiTJCvE
__________________________________
Probability - Uniform Distributions:
https://www.youtube.com/watch?v=KfunVw-0AH0
Probability - Exponential Distributions:
https://www.youtube.com/watch?v=J3KSjZFVbis
Probability - Normal Distributions (Calculus):
https://www.youtube.com/watch?v=gHBL5Zau3NE
Probability - Standard Normal Distributions:
https://www.youtube.com/watch?v=CjF_yQ2N638
Probability - The Law of Large Numbers:
https://www.youtube.com/watch?v=ihTpK6dXSas
___________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
MIT RES.6-012 Introduction to Probability, Spring 2018
View the complete course: https://ocw.mit.edu/RES-6-012S18
Instructor: John Tsitsiklis
License: Creati...
MIT RES.6-012 Introduction to Probability, Spring 2018
View the complete course: https://ocw.mit.edu/RES-6-012S18
Instructor: John Tsitsiklis
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
MIT RES.6-012 Introduction to Probability, Spring 2018
View the complete course: https://ocw.mit.edu/RES-6-012S18
Instructor: John Tsitsiklis
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
View the complete course: http://ocw.mit.edu/6-041SCF13
Instructor: Jimmy Li
Lice...
MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
View the complete course: http://ocw.mit.edu/6-041SCF13
Instructor: Jimmy Li
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
View the complete course: http://ocw.mit.edu/6-041SCF13
Instructor: Jimmy Li
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/e/co...
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/e/constructing-probability-distributions?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Watch the next lesson: https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/v/probability-density-functions?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Missed the previous lesson?
https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/v/discrete-and-continuous-random-variables?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/e/constructing-probability-distributions?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Watch the next lesson: https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/v/probability-density-functions?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Missed the previous lesson?
https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/v/discrete-and-continuous-random-variables?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Get more lessons & courses at http://www.mathtutordvd.com
In this lesson, the student will learn the concept of a random variable in statistics. We will then ...
Get more lessons & courses at http://www.mathtutordvd.com
In this lesson, the student will learn the concept of a random variable in statistics. We will then use the idea of a random variable to describe the discrete probability distribution, which is a key idea used to solve statistics problems.
Get more lessons & courses at http://www.mathtutordvd.com
In this lesson, the student will learn the concept of a random variable in statistics. We will then use the idea of a random variable to describe the discrete probability distribution, which is a key idea used to solve statistics problems.
Random numbers are numbers obtained by some random process. Random variables are called stochastic variable and chance variable. Experiment is a process which g...
Random numbers are numbers obtained by some random process. Random variables are called stochastic variable and chance variable. Experiment is a process which generates raw data. Experiment in which outcomes vary from trial to trial are called random experiments. A variable whose value are determined by outcomes of a random experiment are called random variable.
I am here to teach you the most important subject of your course that is statistics. I hope you will love to my content and i am hopeful and try to present myself in front of you.
Youtube channal https://www.youtube.com/channel/UCcvn...
Face book page https://web.facebook.com/Nazz-Academy...
Instagram https://www.instagram.com/nazzacademy11
Random numbers are numbers obtained by some random process. Random variables are called stochastic variable and chance variable. Experiment is a process which generates raw data. Experiment in which outcomes vary from trial to trial are called random experiments. A variable whose value are determined by outcomes of a random experiment are called random variable.
I am here to teach you the most important subject of your course that is statistics. I hope you will love to my content and i am hopeful and try to present myself in front of you.
Youtube channal https://www.youtube.com/channel/UCcvn...
Face book page https://web.facebook.com/Nazz-Academy...
Instagram https://www.instagram.com/nazzacademy11
This calculus 2 video tutorial provides a basic introduction into probability density functions. It explains how to find the probability that a continuous rand...
This calculus 2 video tutorial provides a basic introduction into probability density functions. It explains how to find the probability that a continuous random variable such as x in somewhere between two values by evaluating the definite integral from a to b. The probability is equivalent to the area under the curve. This video also contains an example problem with an exponential density function involving the mean u which represents the average wait time for a customer in the example problem.
Improper Integrals:
https://www.youtube.com/watch?v=ND9cEdfCFr0
Integration Into Inverse Trig:
https://www.youtube.com/watch?v=AE-0gXXx_j0
Integration of Rational Functions:
https://www.youtube.com/watch?v=4yJmhZBB40w
Integral of Logarithmic Functions:
https://www.youtube.com/watch?v=nrt37LoaSxM
Integrating Exponential Functions:
https://www.youtube.com/watch?v=D9dqdbCgJQM
Integration Formulas:
https://www.youtube.com/watch?v=_KJqeJDb8-I
________________________________
Integration By Tables:
https://www.youtube.com/watch?v=p7KwXMyJK9s
Reduction Formulas - Integration:
https://www.youtube.com/watch?v=LBZcfl97LwY
Center of Mass & Moments:
https://www.youtube.com/watch?v=JSGlBHAGvy4
Center of Mass & Centroid Problems:
https://www.youtube.com/watch?v=SWu_i-19Rn0
Hydrostatic Force Problems:
https://www.youtube.com/watch?v=3jG-hWgUJko
Probability Density Functions:
https://www.youtube.com/watch?v=QKA4HNEw3aY
_________________________________
Normal Distributions - Calculus:
https://www.youtube.com/watch?v=gHBL5Zau3NE
Homogeneous Differential Equations:
https://www.youtube.com/watch?v=ZEJVyybsiT4
1st Order Linear Differential Equations:
https://www.youtube.com/watch?v=gd1FYn86P0c
Bernoulli's Equation for Differential Equations:
https://www.youtube.com/watch?v=BoI_ej-T0V4
Slope Fields:
https://www.youtube.com/watch?v=Wr9VOum9Co0
___________________________________
Converging & Diverging Sequences:
https://www.youtube.com/watch?v=XdkoTb8PEG0
Monotonic & Bounded Sequences:
https://www.youtube.com/watch?v=tHy3TXmZpF0
Calculus Final Exam and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
This calculus 2 video tutorial provides a basic introduction into probability density functions. It explains how to find the probability that a continuous random variable such as x in somewhere between two values by evaluating the definite integral from a to b. The probability is equivalent to the area under the curve. This video also contains an example problem with an exponential density function involving the mean u which represents the average wait time for a customer in the example problem.
Improper Integrals:
https://www.youtube.com/watch?v=ND9cEdfCFr0
Integration Into Inverse Trig:
https://www.youtube.com/watch?v=AE-0gXXx_j0
Integration of Rational Functions:
https://www.youtube.com/watch?v=4yJmhZBB40w
Integral of Logarithmic Functions:
https://www.youtube.com/watch?v=nrt37LoaSxM
Integrating Exponential Functions:
https://www.youtube.com/watch?v=D9dqdbCgJQM
Integration Formulas:
https://www.youtube.com/watch?v=_KJqeJDb8-I
________________________________
Integration By Tables:
https://www.youtube.com/watch?v=p7KwXMyJK9s
Reduction Formulas - Integration:
https://www.youtube.com/watch?v=LBZcfl97LwY
Center of Mass & Moments:
https://www.youtube.com/watch?v=JSGlBHAGvy4
Center of Mass & Centroid Problems:
https://www.youtube.com/watch?v=SWu_i-19Rn0
Hydrostatic Force Problems:
https://www.youtube.com/watch?v=3jG-hWgUJko
Probability Density Functions:
https://www.youtube.com/watch?v=QKA4HNEw3aY
_________________________________
Normal Distributions - Calculus:
https://www.youtube.com/watch?v=gHBL5Zau3NE
Homogeneous Differential Equations:
https://www.youtube.com/watch?v=ZEJVyybsiT4
1st Order Linear Differential Equations:
https://www.youtube.com/watch?v=gd1FYn86P0c
Bernoulli's Equation for Differential Equations:
https://www.youtube.com/watch?v=BoI_ej-T0V4
Slope Fields:
https://www.youtube.com/watch?v=Wr9VOum9Co0
___________________________________
Converging & Diverging Sequences:
https://www.youtube.com/watch?v=XdkoTb8PEG0
Monotonic & Bounded Sequences:
https://www.youtube.com/watch?v=tHy3TXmZpF0
Calculus Final Exam and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
See all my videos at http://www.zstatistics.com/videos
0:00 Intro
0:43 Terminology defined
DISCRETE VARIABLE:
2:24 Probability Mass Function (PMF)
3:31 Cumulative Distribution Function (CDF) - discrete
CONTINUOUS VARIABLE:
7:00 Probability Density Function (PDF)
8:54 Cumulative Distribution Function (CDF) - continuous
This statistics video tutorial provides a basic introduction into cumulative distribution functions and probability density functions. The probability density function or pdf is f(x) which describes the shape of the distribution. It can tell you if you have a uniform, exponential, or normal distribution. The cumulative distribution function or cdf allows you to calculate the area under the curve to the left of some point of interest in order to evaluate the accumulated probability.
Probability Formula Sheet:
https://bit.ly/3zb22rW
Introduction to Probability:
https://www.youtube.com/watch?v=SkidyDQuupA
Probability Formulas:
https://www.youtube.com/watch?v=bddckR734aM
Probability Explained:
https://www.youtube.com/watch?v=UORztmWGY6Q
Probability With Geometry:
https://www.youtube.com/watch?v=DeH5aHWxEaI
Probability of Complementary Events:
https://www.youtube.com/watch?v=0T-CaQCiSf4
Conditional Probability:
https://www.youtube.com/watch?v=sqDVrXq_eh0
__________________________________
Independent and Dependent Events:
https://www.youtube.com/watch?v=lWAdPyvm400
Probability of Mutual Exclusive Events:
https://www.youtube.com/watch?v=X6usGgwXFyU
Multiplication and Addition Rule:
https://www.youtube.com/watch?v=94AmzeR9n2w
Compound Probability:
https://www.youtube.com/watch?v=EHU6pVSczb4
Expected Value:
https://www.youtube.com/watch?v=b6VK2VPMXNI
Probability Tree Diagrams:
https://www.youtube.com/watch?v=w4wKXVwtGac
___________________________________
Bayes Theorem:
https://www.youtube.com/watch?v=OByl4RJxnKA
Probability - Binomial Distribution:
https://www.youtube.com/watch?v=3PWKQiLK41M
Probability - Geometric Distribution:
https://www.youtube.com/watch?v=d5iAWPnrH6w
Probability - Poisson Distribution:
https://www.youtube.com/watch?v=m0o-585xwW0
Continuous Probability Distributions:
https://www.youtube.com/watch?v=QxqxdQ_g2uw
Probability Density Functions:
https://www.youtube.com/watch?v=3xAIWiTJCvE
__________________________________
Probability - Uniform Distributions:
https://www.youtube.com/watch?v=KfunVw-0AH0
Probability - Exponential Distributions:
https://www.youtube.com/watch?v=J3KSjZFVbis
Probability - Normal Distributions (Calculus):
https://www.youtube.com/watch?v=gHBL5Zau3NE
Probability - Standard Normal Distributions:
https://www.youtube.com/watch?v=CjF_yQ2N638
Probability - The Law of Large Numbers:
https://www.youtube.com/watch?v=ihTpK6dXSas
___________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
MIT RES.6-012 Introduction to Probability, Spring 2018
View the complete course: https://ocw.mit.edu/RES-6-012S18
Instructor: John Tsitsiklis
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
View the complete course: http://ocw.mit.edu/6-041SCF13
Instructor: Jimmy Li
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/e/constructing-probability-distributions?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Watch the next lesson: https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/v/probability-density-functions?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Missed the previous lesson?
https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/v/discrete-and-continuous-random-variables?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Get more lessons & courses at http://www.mathtutordvd.com
In this lesson, the student will learn the concept of a random variable in statistics. We will then use the idea of a random variable to describe the discrete probability distribution, which is a key idea used to solve statistics problems.
Random numbers are numbers obtained by some random process. Random variables are called stochastic variable and chance variable. Experiment is a process which generates raw data. Experiment in which outcomes vary from trial to trial are called random experiments. A variable whose value are determined by outcomes of a random experiment are called random variable.
I am here to teach you the most important subject of your course that is statistics. I hope you will love to my content and i am hopeful and try to present myself in front of you.
Youtube channal https://www.youtube.com/channel/UCcvn...
Face book page https://web.facebook.com/Nazz-Academy...
Instagram https://www.instagram.com/nazzacademy11
This calculus 2 video tutorial provides a basic introduction into probability density functions. It explains how to find the probability that a continuous random variable such as x in somewhere between two values by evaluating the definite integral from a to b. The probability is equivalent to the area under the curve. This video also contains an example problem with an exponential density function involving the mean u which represents the average wait time for a customer in the example problem.
Improper Integrals:
https://www.youtube.com/watch?v=ND9cEdfCFr0
Integration Into Inverse Trig:
https://www.youtube.com/watch?v=AE-0gXXx_j0
Integration of Rational Functions:
https://www.youtube.com/watch?v=4yJmhZBB40w
Integral of Logarithmic Functions:
https://www.youtube.com/watch?v=nrt37LoaSxM
Integrating Exponential Functions:
https://www.youtube.com/watch?v=D9dqdbCgJQM
Integration Formulas:
https://www.youtube.com/watch?v=_KJqeJDb8-I
________________________________
Integration By Tables:
https://www.youtube.com/watch?v=p7KwXMyJK9s
Reduction Formulas - Integration:
https://www.youtube.com/watch?v=LBZcfl97LwY
Center of Mass & Moments:
https://www.youtube.com/watch?v=JSGlBHAGvy4
Center of Mass & Centroid Problems:
https://www.youtube.com/watch?v=SWu_i-19Rn0
Hydrostatic Force Problems:
https://www.youtube.com/watch?v=3jG-hWgUJko
Probability Density Functions:
https://www.youtube.com/watch?v=QKA4HNEw3aY
_________________________________
Normal Distributions - Calculus:
https://www.youtube.com/watch?v=gHBL5Zau3NE
Homogeneous Differential Equations:
https://www.youtube.com/watch?v=ZEJVyybsiT4
1st Order Linear Differential Equations:
https://www.youtube.com/watch?v=gd1FYn86P0c
Bernoulli's Equation for Differential Equations:
https://www.youtube.com/watch?v=BoI_ej-T0V4
Slope Fields:
https://www.youtube.com/watch?v=Wr9VOum9Co0
___________________________________
Converging & Diverging Sequences:
https://www.youtube.com/watch?v=XdkoTb8PEG0
Monotonic & Bounded Sequences:
https://www.youtube.com/watch?v=tHy3TXmZpF0
Calculus Final Exam and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
In statistical mechanics, the radial distribution function, (or pair correlation function) in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle.
If a given particle is taken to be at the origin O, and if is the average number density of particles, then the local time-averaged density at a distance from O is . This simplified definition holds for a homogeneous and isotropic system. A more general case will be considered below.
In simplest terms it is a measure of the probability of finding a particle at a distance of away from a given reference particle, relative to that for an ideal gas. The general algorithm involves determining how many particles are within a distance of r and r+dr away from a particle. This general theme is depicted to the right, where the red particle is our reference particle, and blue particles are those which are within the circular shell, dotted in orange.