The content you made is really great but your speaking too fast and it sounds as if you are swallowing your words.....its a bit teasing as we have to pause and try to understand...may be you make the pronunciation more clearer. just my opinion, I dont know if others too felt it.
It is interesting that even though you're using manim, your style is very unique. You're with a sans-serif font, a different color palette, and layout throughout the "slides" is also different. Ever since manim got released and documented, there has been no shortage of 3b1b-like content (which is cool), but all of them suffer from the same thing: they all look like a worse copy 3b1b video when it comes to aesthetics.
That was a great video, I loved the content and the visuals and the style as well, and you explained the formulas amazingly well. It would've been great to see what the "infinitesimally small chance of the event not happening" would mean in the strong law, e.g. "It is technically possible, but infinitesimally probable, that your samples are not representative of the distribution. Kinda like flipping heads twice as often as tails, after a million coin flips with a true coin." Overall, great experience, looking forward to the next one.
But why the limit goes to infinity and not to the total number of the population? Are we assuming the population is infinite? I would think that if the population has a finite size, the mean of the sample would get the true mean of the population as the sample size approaches the population size
It does, and it mostly comes down to how you define something as converging in probability versus almost surely converging. The interpretations for a limit of a probability and a probability of a limit are very subtlety different, but it is important in this case. This is a good thread that explains the difference: math.stackexchange.com/questions/2784153/limit-of-probability-and-probability-of-limit
Only good for people that already know the content. For everybody else it is too fast not very well explained. Also you speak so fast, that I had the repeat some parts of the video up to four times to understand what you were saying.
probability of not picking an integer in [0,100] wont exactly be 1 right - it will tend to 1 so saying that probability of 1 means that theres an infinitesimal chance of it not happening is correct right? if a probability is *exactly* 1 then it will always happen if it tends to 1 then it might not happen is this correct?
As far as I am aware, events like not picking an integer in this example would just be referred to as exactly having a probability of one because of the way infinitesimal values work. You don't generally say things will absolutely happen in higher-level statistics due to some concepts in measure theory that I frankly don't have enough background in yet.
well the probability of not picking an integer in this scenario is a real number and not a sequence, so it doesn't really make sense to says that this number "tends to 1". it is either 1 or not. (and it is fairly easy to prove that it cannot be something other than 1). it cannot be "infinitesimally close to 1" either, since in this context, all numbers are real, and real numbers simply don't have a concept of infinitesimals. what we call "infinitesimals" in the context of the real numbers are simply variables that are part of a bigger expression that will make them approach 0. rigorously speaking, only a very few spaces have infinitesimals (for example the hyperreal numbers), but these are extremely niche topics and the term "infinitesimal" is often used to say "number really close to 0" (like 10^-1000 for instance)
@@nstatum8290 I can chip in there. Measure theory is basically the backbone of probability, as well as geometry. In measure theory 'almost every' has a very precise meaning. It means that the set containing the events that negate your statement have measure zero. A good example is the one you gave. The subset of integers on [0,100] has measure 0, so that means 'almost every' number on that interval is not an integer. The same statement would be false for an interval like [0,10^-100]. It doesn't necessarily relate to cardinality either, as you have sets of measure 0 with cardinality equal to that of the reals(like cantors set). Technically you need to first define a measure and a set of sets that is 'measurable' used as the domain of the measure. But these are obvious given any particular distribution.
The content you made is really great but your speaking too fast and it sounds as if you are swallowing your words.....its a bit teasing as we have to pause and try to understand...may be you make the pronunciation more clearer. just my opinion, I dont know if others too felt it.
this comment represents all the viewers
I disagree - people have different accent(Indian accent & British accent - just watchore video get used to it) if I are not that fast watch in 0.5x 😂
The video is great, it’s just one problem, the voice over. Sometimes it’s to fast, sometimes it’s unclear.
It is interesting that even though you're using manim, your style is very unique. You're with a sans-serif font, a different color palette, and layout throughout the "slides" is also different. Ever since manim got released and documented, there has been no shortage of 3b1b-like content (which is cool), but all of them suffer from the same thing: they all look like a worse copy 3b1b video when it comes to aesthetics.
Thank you! I think you're absolutely right, and I did try to put at least a little bit of thought into making a distinct style when I was starting
@@nstatum8290 Keep it up with the good content. A channel like yours is a true inspiration for me
@@nstatum8290 I'm going to be honest, I didn't even notice it was Manim
That was a great video, I loved the content and the visuals and the style as well, and you explained the formulas amazingly well. It would've been great to see what the "infinitesimally small chance of the event not happening" would mean in the strong law, e.g. "It is technically possible, but infinitesimally probable, that your samples are not representative of the distribution. Kinda like flipping heads twice as often as tails, after a million coin flips with a true coin."
Overall, great experience, looking forward to the next one.
Try to speak clearly bro....this is something that can help anyone around the world ..i had to slow the video and even then u weren't clear enough
loud and clear to me
This is a very cool video! It got many key points across that are sometimes confused, and the explanation is also really good.
Great video. One of the few videos I don't watch on 1.5x speed.
Also compliments that the video has a unique style.
I like it.
One of the videos i don’t watch on *2 but on *1.5
Nice video and well explained. However it is so difficult to understand you. So fast and not very clear :(
Such a beautiful video and the explanation was even more beautiful!
Thanks!!
This is well put together and conveys a lot of information but I am begging you, please slow down when you speak.
Yeah sincere apologies about that, I've been trying to work on it, and I think I'll have the correct pace hammered down within the next 2 or 3 videos
@@nstatum8290 Thank you!
Great job at explaining the nuances of P = 0 and P = 1. As someone studying some graduate level measure theory, I much prefer your definition lol.
0:01, please try to speak more clearly. I listened twice and have no idea what you said.
Great video. Also I hope you sign up for a diction and modulation course to help out with that pronunciation
So the weak law says that you can take enough samples so that you have an arbitrary probability
Awesome video. Thank you so much
Very nice, very cool, very swag
wow ! really helpful video!thanks :)
But why the limit goes to infinity and not to the total number of the population? Are we assuming the population is infinite? I would think that if the population has a finite size, the mean of the sample would get the true mean of the population as the sample size approaches the population size
Great video, thanks
Very useful! Thanks
Does the limit being inside/outside of the probability make a difference?
It does, and it mostly comes down to how you define something as converging in probability versus almost surely converging. The interpretations for a limit of a probability and a probability of a limit are very subtlety different, but it is important in this case. This is a good thread that explains the difference: math.stackexchange.com/questions/2784153/limit-of-probability-and-probability-of-limit
How about math of clusters?
That's a great idea! I will definitely look into it
If I could give an advice, I think you should speak a little slower for the non-fluent English speakers. Other than that, good video!
what softwares do you use for these videos?
also good job!
Thanks! And I use a mix of After Effects and Manim which is a Python Package
Only good for people that already know the content. For everybody else it is too fast not very well explained. Also you speak so fast, that I had the repeat some parts of the video up to four times to understand what you were saying.
Has it been discovered in some axiom system like ZFC or is it an additional axiom in probability?
great video
probability of not picking an integer in [0,100] wont exactly be 1 right - it will tend to 1
so saying that probability of 1 means that theres an infinitesimal chance of it not happening is correct right?
if a probability is *exactly* 1 then it will always happen
if it tends to 1 then it might not happen
is this correct?
As far as I am aware, events like not picking an integer in this example would just be referred to as exactly having a probability of one because of the way infinitesimal values work. You don't generally say things will absolutely happen in higher-level statistics due to some concepts in measure theory that I frankly don't have enough background in yet.
well the probability of not picking an integer in this scenario is a real number and not a sequence, so it doesn't really make sense to says that this number "tends to 1". it is either 1 or not. (and it is fairly easy to prove that it cannot be something other than 1).
it cannot be "infinitesimally close to 1" either, since in this context, all numbers are real, and real numbers simply don't have a concept of infinitesimals. what we call "infinitesimals" in the context of the real numbers are simply variables that are part of a bigger expression that will make them approach 0.
rigorously speaking, only a very few spaces have infinitesimals (for example the hyperreal numbers), but these are extremely niche topics and the term "infinitesimal" is often used to say "number really close to 0" (like 10^-1000 for instance)
@@nstatum8290 I can chip in there. Measure theory is basically the backbone of probability, as well as geometry. In measure theory 'almost every' has a very precise meaning. It means that the set containing the events that negate your statement have measure zero.
A good example is the one you gave. The subset of integers on [0,100] has measure 0, so that means 'almost every' number on that interval is not an integer. The same statement would be false for an interval like [0,10^-100]. It doesn't necessarily relate to cardinality either, as you have sets of measure 0 with cardinality equal to that of the reals(like cantors set).
Technically you need to first define a measure and a set of sets that is 'measurable' used as the domain of the measure. But these are obvious given any particular distribution.
very good
awesome
Perhaps it should be called the law of a large number of numbers.
So Latin alphabet mu is mean.
Yeah exactly, specifically it refers to the mean of the population rather than the mean of a sample from that population
Except μ is a letter of the greek alphabet, not the latin
@@fuuryuuSKK Ahha thanks for your feedback.
Beautiful
Why mumble
Your speech is too fast