In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity. The difference between a probability measure and the more general notion of measure (which includes concepts like area or volume) is that a probability measure must assign value 1 to the entire probability space.
Intuitively, the additivity property says that the probability assigned to the union of two disjoint events by the measure should be the sum of the probabilities of the events, e.g. the value assigned to "1 or 2" in a throw of a die should be the sum of the values assigned to "1" and "2".
Probability measures have applications in diverse fields, from physics to finance and biology.
Definition
The requirements for a function μ to be a probability measure on a probability space are that:
μ must return results in the unit interval [0, 1], returning 0 for the empty set and 1 for the entire space.
A brief introduction to probability spaces and random variables.
Princeton COS 302, Lecture 15, Part 2
published: 01 Apr 2020
Risk neutral probability measure simplified
#research #review #learning
published: 09 Nov 2022
Probability Theory Tutorial 3 - Probability Measures and Properties
Probability Tutorials: https://www.kindsonthegenius.com/2019/03/25/basics-of-conditional-probability/
published: 04 Apr 2019
Probability and Measure Lecture 1: What is a Measure?
In this video, we introduce some of the main definitions in Measure theory. This includes measures and sigma-fields and some examples to set the stage for future lectures.
Written Lecture Notes can be found at https://sites.ualberta.ca/~kashlak/
published: 26 Feb 2022
Lecture 07 : Probability Measures
published: 02 Aug 2021
Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2
An introduction to probability density functions
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/thanks
Curious about measure theory? This does require some background in real analysis, but if you want to dig in, here is a textbook by the always-great Terence Tao.
https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf
Also, for the real analysis buffs among you, there was one statement I made in this video that is a rather nice puzzle. Namely, if the probabilities for each value in a given range (of the real number line) are all non-zero, no matter how small, their sum will be infinite. This isn't immediately obvious, given ...
published: 12 Apr 2020
Measure Theoretic Probability, Lesson 1
Fields and sigma fields!
published: 06 Apr 2023
Probability of Complementary Events & Sample Space
This video tutorial explains how to calculate the probability of complementary events as well as AND/OR events using the sample space of a six-sided die.
Probability - Free 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: ...
published: 23 Mar 2019
Measure Theoretic Probability: Lesson 24
More Properties of Expectation, Independence for Random Variables, Passing Infinite Sums Through Expectations
In this video, we introduce some of the main definitions in Measure theory. This includes measures and sigma-fields and some examples to set the stage for futu...
In this video, we introduce some of the main definitions in Measure theory. This includes measures and sigma-fields and some examples to set the stage for future lectures.
Written Lecture Notes can be found at https://sites.ualberta.ca/~kashlak/
In this video, we introduce some of the main definitions in Measure theory. This includes measures and sigma-fields and some examples to set the stage for future lectures.
Written Lecture Notes can be found at https://sites.ualberta.ca/~kashlak/
An introduction to probability density functions
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply...
An introduction to probability density functions
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/thanks
Curious about measure theory? This does require some background in real analysis, but if you want to dig in, here is a textbook by the always-great Terence Tao.
https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf
Also, for the real analysis buffs among you, there was one statement I made in this video that is a rather nice puzzle. Namely, if the probabilities for each value in a given range (of the real number line) are all non-zero, no matter how small, their sum will be infinite. This isn't immediately obvious, given that you can have convergent sums of countable infinitely many values, but if you're up for it see if you can prove that the sum of any uncountable infinite collection of positive values must blow up to infinity.
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
An introduction to probability density functions
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/thanks
Curious about measure theory? This does require some background in real analysis, but if you want to dig in, here is a textbook by the always-great Terence Tao.
https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf
Also, for the real analysis buffs among you, there was one statement I made in this video that is a rather nice puzzle. Namely, if the probabilities for each value in a given range (of the real number line) are all non-zero, no matter how small, their sum will be infinite. This isn't immediately obvious, given that you can have convergent sums of countable infinitely many values, but if you're up for it see if you can prove that the sum of any uncountable infinite collection of positive values must blow up to infinity.
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
This video tutorial explains how to calculate the probability of complementary events as well as AND/OR events using the sample space of a six-sided die.
Proba...
This video tutorial explains how to calculate the probability of complementary events as well as AND/OR events using the sample space of a six-sided die.
Probability - Free 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/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
This video tutorial explains how to calculate the probability of complementary events as well as AND/OR events using the sample space of a six-sided die.
Probability - Free 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/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
In this video, we introduce some of the main definitions in Measure theory. This includes measures and sigma-fields and some examples to set the stage for future lectures.
Written Lecture Notes can be found at https://sites.ualberta.ca/~kashlak/
An introduction to probability density functions
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/thanks
Curious about measure theory? This does require some background in real analysis, but if you want to dig in, here is a textbook by the always-great Terence Tao.
https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf
Also, for the real analysis buffs among you, there was one statement I made in this video that is a rather nice puzzle. Namely, if the probabilities for each value in a given range (of the real number line) are all non-zero, no matter how small, their sum will be infinite. This isn't immediately obvious, given that you can have convergent sums of countable infinitely many values, but if you're up for it see if you can prove that the sum of any uncountable infinite collection of positive values must blow up to infinity.
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
This video tutorial explains how to calculate the probability of complementary events as well as AND/OR events using the sample space of a six-sided die.
Probability - Free 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/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity. The difference between a probability measure and the more general notion of measure (which includes concepts like area or volume) is that a probability measure must assign value 1 to the entire probability space.
Intuitively, the additivity property says that the probability assigned to the union of two disjoint events by the measure should be the sum of the probabilities of the events, e.g. the value assigned to "1 or 2" in a throw of a die should be the sum of the values assigned to "1" and "2".
Probability measures have applications in diverse fields, from physics to finance and biology.
Definition
The requirements for a function μ to be a probability measure on a probability space are that:
μ must return results in the unit interval [0, 1], returning 0 for the empty set and 1 for the entire space.
The Reserve Bank of India (RBI) on Monday doubled down on its liquidity injection measures for the ... This will probably be the first time that a VRR auction for such a long tenor will be conducted.
Daily water testing, removal of pooja waste among measures to keep Ganga 'dip-safe'. “We know that at this point of time that this is probably the best place not just in the country or in the world but ...
“If anything does happen, it’ll probably start in the states already leaning toward these more hostile measures,” said Jason de León, a professor of anthropology and Chicana/Chicano studies at UCLA.
Use of Non-IFRS Measures and Non- GAAP Measures ...Underground accumulations of hydrocarbons cannot be measured in an exact manner and estimates thereof are a subjective process aimed at understanding the statistical probabilities of recovery.
For Brentford, there was a measure of relief. It’s probably fair to say that the run of one win in nine games in which they went into this weekend was not representative of how they’d played but, ...
For Brentford, there was a measure of relief. It’s probably fair to say that the run of one win in nine games in which they went into this weekend was not representative of how they’d played but, ...
We have to reiterate that any of the serious cabal players at this point – if we see them bleating on social media – have probably ‘gone’ under EO 13818, and are LONG GONE.
Under Janson's leadership, Cabool has the highest AnnualPerformanceReport score — which measures students' academic performance and other factors — of any district in Texas County. "We have probably ...
In the second part of their study, they asked participants to read other people’s rants and measured how this affected their mood ... As you probably anticipated, the results showed that ranting led most ...
We’d probably be better off if we did ... What do you make of how Severance presents at-work disciplinary measures?. That’s probably the most out-there aspect of the show ... In real life, we probably wouldn’t ...
In the other response, weather risks are reduced by lowering the probability of impact when a weather extreme occurs. This is achieved by measures like flood control, building standards and strategic retreat from danger zones.
J.K ... “We are just addressing temporary things that probably should happen for the city’s best interests, as well as Ms ... One of those temporary measures commissioners adopted was appointing Harding as the interim city clerk.
Polling shows lukewarm support among Metro voters for a potential measure. In a November survey, only 51% of potential voters who were given a title and short description of the measure said they would definitely or probably support the measure.
Show Caption. Hide Caption ... When norovirus cases spike, these are symptoms you should watch out for, and measures you can take for prevention. If you feel a sudden urge to run to the bathroom and lose your lunch, you're probably not the only one ...