This a re-upload of this part because the original video had a small mistake that Timothy Zhou found. Thanks! The old version is still online if you want to read the comments: ruclips.net/video/W7wnSPn9mk8/видео.html
Hey Julian, first off all thanks for your videos (especially on measure theory); they help me a great deal with my master thesis. I was wondering if you are planning to make a video on the mixed / other cases any time soon? I'm constantly running in to problems when I have continuous distributions that overlap with Dirac delta's, and it bugs me that I don't know if I'm handling them in a decent way.
Thank you very much! Mixed cases are not a mystery when you just deal with abstract measure theory. You can just calculate with the probability measure and the corresponding Lebesgue integral.
@@brightsideofmaths What if I want to use Monte Carlo integration? It's easy to create some (mixed) function that lets me get some points for my MC integration. However how can I make this (mixed) function so that the sampled points are considered uniform (which is a requirement for the most basic MC integration)? Also I have to compare multiple probability distributions at these points. If I use probability mass than continuous distributions are all considered 0 (so not really comparable), but if I use probability density than delta's explode to infinity and become incomparable. This would lead to first having to check probability mass, and afterwards checking probability density, which sounds ugly to me. I could circumvent this by using probability mass on tiny intervals, but of course this doesn't really pair well with the idea of using Monte Carlo integration in the first place...
Thanks a lot for your videos. I watched the probability and measure theory playlists and it helped me a lot. I was wondering if by any chance you planned on developing the mixed case?
@@brightsideofmaths You got me wrong, I don't need em:P I meant before you make all of them again in german, just throw german subs under them (as you apparently did) for german people if they cant understand english, which would be weird at this level of math but anyway ^^
I assume that we could say the probability measure in the discrete case is also an integral over the sample space, but with respect to the counting measure instead of the Lebesgue measure. Also unless I'm missing something, the definition of the pdf as a measurable map from the sample space to R seems to be the same definition as a (concrete) random variable, but just with the additional requirement of having an integral of 1. Does this mean that pdfs are random variables, and can we treat them as such? Is there such thing as a distribution or expectation of a pdf?
In the descrete case, when Omega contains countable infinity elements: Isn't the probability of a single event also 0? In your example if Omega = naturalNumbers isn't the probability to "draw" a 5 equal to 0?
Thanks for doing this, i have Einführung in die Wahrscheinlichkeitstheorie und Statistik right now. But my German isn't too good. So this really helps.
@@brightsideofmaths Yeah, i'm doing an exchange year at TUM in München, and my home university forced me to take statistics, which i only found in German
I am going to follow your 18 videos but want to know what is the general pattern of probability at undergrad and gradute level probability. Mainly i came to know that probability is studied as an area of mathematical analysis from undergraduate level. Previously here in india we studied probability basic definitions and bayes theorem at high school level algebra. But i dont know how to follow the pattern that takes to measure theoretical level as i already have done graduate real analysis course called measure theory and lebesgue integration etc. Any specific pattern of chapters and books you suggest.
A year ago, I published every video in German and in English. However, the German one was rarely watched and I decided that it would be better to use my time to produce a new video instead of doing the same thing again just in a different language. However, I still like the idea to offer a lot of options and some day I will translate the videos for sure.
Is it true that "probability of a singe point is just zero because we have uncountably many points on dart"? For this reason we must deal with probability for regions.
In the case of dart, we have uncountable many points and probability for regions is more useful. The probability to hit a given point is zero but this does not mean that it is impossible. That is the important distinction we have here in contrast to a finite sample space Omega.
@@brightsideofmaths Not boring this video is so well done. It was incredibly hard to find a measure theoretic explanation of this until this video. Thank you so much for making this video it is a gift to students learning measure theoretic probability
![Felix "Unfair" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/Oswujxm2Ag0/mqdefault.jpg)
This a re-upload of this part because the original video had a small mistake that Timothy Zhou found. Thanks!
The old version is still online if you want to read the comments: ruclips.net/video/W7wnSPn9mk8/видео.html
i love how easily digestible these videos are. These are really going to help me in my Distribution theory and inference class at FSU
Thank you! And thanks for your support :)
As the series progresses will you cover (for completeness) the Essential Supremum?
Hey Julian, first off all thanks for your videos (especially on measure theory); they help me a great deal with my master thesis.
I was wondering if you are planning to make a video on the mixed / other cases any time soon? I'm constantly running in to problems when I have continuous distributions that overlap with Dirac delta's, and it bugs me that I don't know if I'm handling them in a decent way.
Thank you very much! Mixed cases are not a mystery when you just deal with abstract measure theory. You can just calculate with the probability measure and the corresponding Lebesgue integral.
@@brightsideofmaths What if I want to use Monte Carlo integration? It's easy to create some (mixed) function that lets me get some points for my MC integration. However how can I make this (mixed) function so that the sampled points are considered uniform (which is a requirement for the most basic MC integration)?
Also I have to compare multiple probability distributions at these points. If I use probability mass than continuous distributions are all considered 0 (so not really comparable), but if I use probability density than delta's explode to infinity and become incomparable. This would lead to first having to check probability mass, and afterwards checking probability density, which sounds ugly to me. I could circumvent this by using probability mass on tiny intervals, but of course this doesn't really pair well with the idea of using Monte Carlo integration in the first place...
Thanks a lot for your videos. I watched the probability and measure theory playlists and it helped me a lot. I was wondering if by any chance you planned on developing the mixed case?
Yes, we will talk about the mixed case in future.
I am sorry, I got lost when you set f(x) = 1/2 in the example of the continuous function... Could you elaborate a little more on that? Thanks!!
It's an example. You can check that all properties of a probability measure are satisfied. In particular we have P(Omega) = 1.
@@brightsideofmaths just write subtitles for the people i guess
@@deyomash This video has subtitles :)
@@brightsideofmaths You got me wrong, I don't need em:P I meant before you make all of them again in german, just throw german subs under them (as you apparently did) for german people if they cant understand english, which would be weird at this level of math but anyway ^^
I assume that we could say the probability measure in the discrete case is also an integral over the sample space, but with respect to the counting measure instead of the Lebesgue measure.
Also unless I'm missing something, the definition of the pdf as a measurable map from the sample space to R seems to be the same definition as a (concrete) random variable, but just with the additional requirement of having an integral of 1. Does this mean that pdfs are random variables, and can we treat them as such? Is there such thing as a distribution or expectation of a pdf?
We discuss random variables later in the series :)
@@brightsideofmaths Yes, I was revisiting this video after watching the later ones in the series
@@sinx2247 So then you know that a pdf is not a random variable but a pdf can describe a random variable or define one.
I'm assuming that before conditional probability the subject of dependence and non equiprobable events will be addressed a little further?
Yes, indeed :)
Pdf file possible of this video sir@@brightsideofmaths
Hey Julian, which software you use for your presentations? It think like a board and I need it to do math and data science lessons. Can you help me?
Xournal :)
In the descrete case, when Omega contains countable infinity elements: Isn't the probability of a single event also 0? In your example if Omega = naturalNumbers isn't the probability to "draw" a 5 equal to 0?
No, the probability of the whole space has to be 1. That is not possible if all singletons would have probability 0. (in the discrete case)
There is no uniform probability measure on the space (N, P(N)), but some singletons (at least 1) must satisfy P({x}) > 0.
Danke sehr!!
Thanks for doing this, i have Einführung in die
Wahrscheinlichkeitstheorie und Statistik right now. But my German isn't too good. So this really helps.
You are very welcome. I need to take a German course?
@@brightsideofmaths Yeah, i'm doing an exchange year at TUM in München, and my home university forced me to take statistics, which i only found in German
@@alfabetet7489 In this case I really think that my series here can help you :)
@@brightsideofmaths Definitely :)
I am going to follow your 18 videos but want to know what is the general pattern of probability at undergrad and gradute level probability. Mainly i came to know that probability is studied as an area of mathematical analysis from undergraduate level. Previously here in india we studied probability basic definitions and bayes theorem at high school level algebra. But i dont know how to follow the pattern that takes to measure theoretical level as i already have done graduate real analysis course called measure theory and lebesgue integration etc. Any specific pattern of chapters and books you suggest.
My course is in between basic and advanced. I do the ground work and put in measure theoretical aspects.
The Videos are so great, thank you! Maybe they could upload in german too? ... That would be awesome!!
A year ago, I published every video in German and in English. However, the German one was rarely watched and I decided that it would be better to use my time to produce a new video instead of doing the same thing again just in a different language. However, I still like the idea to offer a lot of options and some day I will translate the videos for sure.
Is it true that "probability of a singe point is just zero because we have uncountably many points on dart"? For this reason we must deal with probability for regions.
In the case of dart, we have uncountable many points and probability for regions is more useful. The probability to hit a given point is zero but this does not mean that it is impossible. That is the important distinction we have here in contrast to a finite sample space Omega.
@@brightsideofmaths ruclips.net/video/ZA4JkHKZM50/видео.html It's related.
@@BatuhanBayr Yes, perfect video for this!
super boring
What exactly? :)
@@brightsideofmaths Not boring this video is so well done. It was incredibly hard to find a measure theoretic explanation of this until this video. Thank you so much for making this video it is a gift to students learning measure theoretic probability