But what is the Central Limit Theorem?

Using Heads (+) or Tails (-), a coin could simulate a Galton board with infinitely narrow nails.. just a thought.

Question: what would happen if you move the opening of the dropper side ways?
It seems to me that it is rather fairly simple phenomena, the central bars are filled more because more and more balls are being dropped at center rather than side. Fairly logical reasoning.

You should include also a references for your video in the description
Good video and good work

You are awesome, Im studying online and your videos are better than everything, Do you have a patreon?

il faut bien préciser que la "planche de Galton" fait tomber les billes au départ toujours sur le même barreau ce qui définit "une population" bien précise, si je change de barreau j'obtiens une nouvelle population. Ce raisonnement explique pourquoi les statisticiens essaient de voir si certains tirages appartiennent à une population différente en comparant leur valeur avec la valeur standard supposée de la population étudiée. Cette "loi" est théorique, parque qu'au départ de l'expérience, "dans la réalité", on ne sait pas sur quel barreau la bille est tombée.

Why would someone dislike this? What is their problem? 😂
This video was awesome

it's not that mind boggling when you think about it, it's like blurring something over and over, as it gets smeared it loses its original detail / shape.

Has he done a video about the distribution curve for non-identical variables?

Where does the sqrt(2) come from in the formula?

Please make more videoos ! Your work is truly awesomee.

>Galton Board
But the balls are falling all at once pushing eachother to the sides. What if they were falling one ball at a time?

If we characterize the series of histograms in the video as a sequence of piecewise constant functions, does this sequence of functions converge pointwise to the standard Gaussian density? If so why? Does anyone have any reference?

Thank you for this great video. It was greatly intuitive as well as engrossing too. Didn't even feel that 30 minutes had passed by at the end of the video.

Beautiful breakdown of the normal distribution formula. I'm in intro to statistics and that was great to watch

One day I want to be big brain enough to understand this

Thank you very much for doing this. I love how you make heavy ideas simple to digest.

Most clear explanation of CLT I have ever seen

À la roulette au casino ça fonctionne la théorie ? Moi je gagne souvent en misant les chiffres qui sont en face du dernier chiffre sur lequel la bille est tombée

Your beginning example dont fit the 3 assumptions given how random numbers are numerically calculated in computers. Same as the Galton board you still violates some assumptions of the CLT which makes this more interesting on how complicated it is to determine Normal Distribution.

really good explaination

It turns quanta into waves

Thank for your sharing <3 I'd love to ask a question. Why there is the (1/2) in the power of e in the formula of normal distribution?

The bell at 7.15 looks to me skewed to the right actually

Hope to see a video explaining the chi-square distribution，t distribution and f distribution visually. The theory in the book is so boring and incomprehensible. Thanks very much！

Does this mean that I can always perform ANOVA provided homocedasticity is true? Whether or not normality is true?

I would argue that a fourth major assumption of the CLT (particularly in practical applications) is that a test population is sufficiently (admittedly, that is a bit subjective) large in order to represent a true population. This is likely one (of many) explanations for the Galton board behaving how it does, despite physics.

Would it be possible to make a set of differently weighted dice that would make the probability of all the possible outcomes equal?

It seems like Conservation Energy/Mass

BTW, subscribed!

Hello! I would like to use this video in my statistics class, do I have your permission? Thank you for the amazing work.

Just wanted to stand in line with other university professors praising your content. I am an MD and am involved with clinical trials, registry-based, and epidemiological studies. I work with probabilities, and normal distributions, and had to understand the central limit theorem on a practical level. I am fairly successful in my career because it looks like I've built quite a good intuition, however connecting the math to my experience, and basically giving a name to the things I encountered is just a whole new level. Due to this, I consider this video (and a lot of your videos) art, as others said before. The explanation and the visualization are just perfect. Hats off to you!

Animation is Concept clarifying!!!! Which app do you use?

Work of art 🎭

When your crush (now SO) teaches you stats in maths and is very passionate so you gotta put in the work and the hours to actually know whats going on😅
They sent a link to 3 of these videos so I now have a starting point👌

I would like to know what may happen when using a galton board with all the balls are released by taking off a tab where all the balls feely fall ocupying the width of the board insted of falling from a centered hole alinged with the Y axis of the bellshape

thank you sir

Thanks

best channel

Heteroskedasticity what now?

Technically the Galton board approximates the Gaussian distribution. It actually demonstrates a binomial distribution with a large value for n. Of course that means it's converging on a Gaussian distribution, and I'm purposefully being a pedant.

Thanks. Please more probabilities and statistics ❤

Well, I was wondering why is the probability they the ball will either go to the left or to right is 50 percent. Using physics we can know the impact on the ball and predict the right direction and its final position where the ball will fall into.....