And adding more nails is a representation of the central limit theorem: As the ball falls it is essentially creating a list of (supposedly independent) random variables. {X1,X2,....Xn} Where Xi is +1 if it falls right and 0 if it falls left. Adding these up tells you which space it will fall into. Central theorem says as long as n is sufficiently big then the sum will be approximately normal. So the number of rows of nails that the ball passes has to be large for it to be approximately normal
Very nice everything, except the "theoretical curve' drawn in 1:53. That is NOT the shape of the PDF of a normal distribution, the slope in both sides is way too constant.
Note that many more drops than you have balls for can be simulated: Run the experiment many times, tallying the falls in each bin, add the individual bin tallies.
Hope that kind of helps. It might be good to read about the law of large numbers and the central limit theorem as that is essentially what is going on here.
True, but the number of balls increases the approximation of the binomial distribution to be closer to a normal distribution as you are increasing the number of trails.
The input is biased because it is put in the center. So we can say in normal distribution, there is a preferred/biased input and result. What would be the result is the balls can be fed from anywhere top of Galton board.
Ok... take a thousand Galton boards. Run them. For each one, measure how many balls were in the "wrong" place for it to form a perfect Binomial bell-curve distribution. How many of the boards were off by just one ball, how many were off by just 2, etc. Graph it, number of "wrong" balls as X, number of boards with that many "wrong", as Y. What shape would that graph have? AKA someone program it into Wolfram for me cos I haven't a bleedin' clue how to. Unless it's a well-known problem, not a mathematician here.
"We can accurately predict the overall pattern for lots of them... that pattern is called the Normal Distribution"... all while the balls form two separate peaks... Ladies and gentlemen, I give you... the Parker Bell Curve.
Looking at the reddish scar, there is a good probability that he assembled the board just hours before he recorded this vid. Did it in a hurry and a nail scratched his hand..
For more balls, better approximation of a normal distribution, so more balls = closer to the normal distribution curve. As for more pegs, its probably a similar story, but im not sure.
It is so easy It called Galton board. It made by colorless balls. After that used a computer simulation program. In details: The process is done with all balls of white colour. After that, recording video for the balls are landed in each section at the bottom. Finally, effects of a computer colour simulation program is done for the recorded video.
is it just me or maybe its also just because of gravity? the balls are drawn towards the middle because its more likely to follow the downward path than the sideway path?
The only time they move 'down' is after they have selected to go left or right. There is a 50% chance to go left or right each time. Gravity does not make a ball go left then right then left. Over 12 50% chances or left or right you would expect it to have gone left 50% and right 50% leaving it in the middle. Obviously with the way probability works this will never work out exactly, but more often than not the position will be towards the middle.
No, not really.What if there was one peg and only two spaces for balls to drop into, would it look normal then? No, it would just be 50/50. Adding more balls is showing how the "Law of large numbers" works which Bernoulli proved. Basically, this says that performing the experiment loads of times we will get close to the expected value. So the histogram of the walls will fit close to the actually distribution (whether it is normal or not)....
You mention the number of paths, but if it were a rectangular board extending infinitely to the sides, you would see the same pattern. The balls are clustering around the gravitational vector.
From varsity I'm here wow..
This means I am at last module of option trading course.lol
Same !!
Zerodha
Congratulations we are above the average.😀... I knew random, and normal distribution... but didn't know this experiment.
I m too
this just blows my mind every time i see it.
Matt! What a surprise to find you here.
And adding more nails is a representation of the central limit theorem:
As the ball falls it is essentially creating a list of (supposedly independent) random variables. {X1,X2,....Xn}
Where Xi is +1 if it falls right and 0 if it falls left. Adding these up tells you which space it will fall into.
Central theorem says as long as n is sufficiently big then the sum will be approximately normal. So the number of rows of nails that the ball passes has to be large for it to be approximately normal
We all have this 'normal distribution' chapter in our school...
Protect this guy by all cost!
All from Team Zerodha Varsity, Let's Gooo🚀🚀🚀
Very nice everything, except the "theoretical curve' drawn in 1:53. That is NOT the shape of the PDF of a normal distribution, the slope in both sides is way too constant.
Anyone here from Zerodha Varsity?? 😉
Note that many more drops than you have balls for can be simulated: Run the experiment many times, tallying the falls in each bin, add the individual bin tallies.
So is it a case of More balls = better representation of the distribution
and more nails = closer to the normal distribution?
How to get 24000 on lina's ball
Where can I buy one of those Galton boards. Have been looking for that and your version is the one I like the most!
Hope that kind of helps. It might be good to read about the law of large numbers and the central limit theorem as that is essentially what is going on here.
but if you are dropping them in the middle they are more likely to finish in the middle right?
Fascinating stuff.. thanks.
True, but the number of balls increases the approximation of the binomial distribution to be closer to a normal distribution as you are increasing the number of trails.
Merhaba bir proje için boyutlara ihtiyacın var Rica etsem çiviler arasındaki mesafeden ve kutunun boyutu hakkında bilgi verebilir misiniz?
The input is biased because it is put in the center. So we can say in normal distribution, there is a preferred/biased input and result. What would be the result is the balls can be fed from anywhere top of Galton board.
Ok... take a thousand Galton boards. Run them. For each one, measure how many balls were in the "wrong" place for it to form a perfect Binomial bell-curve distribution. How many of the boards were off by just one ball, how many were off by just 2, etc.
Graph it, number of "wrong" balls as X, number of boards with that many "wrong", as Y. What shape would that graph have? AKA someone program it into Wolfram for me cos I haven't a bleedin' clue how to. Unless it's a well-known problem, not a mathematician here.
Where can I buy this board? Looked everywhere, can't find anything this big
buy nails and a hammer
Ok what next
Buy a board.
Also great example of the large number theory:)
From varsity to here
easy to understand ! appreciate that !
dota 2 lina's ball brought me here
no barrier here
same but dota 2 is rigged
Whatever destination will have the higher no of paths will end up getting lots and lots of people into it
WTF It's Matt Parker!
"We can accurately predict the overall pattern for lots of them... that pattern is called the Normal Distribution"... all while the balls form two separate peaks... Ladies and gentlemen, I give you... the Parker Bell Curve.
He apparently used it to demonstrate regression to the mean, something I still don't understand.
@@Competitive_Antagonist You can read more about regression to the mean in Thinking Slow and Fast psychology book...
the jump cut at 0:40 tells me that the two balls did in fact end up in the same position in that instance
Where the people from varsity at?
yupp
Here,, I'm
How many of you have come to watch this video from Varsity😂
Hahaha
Why woud number of balls not also help? wouldnt it not resemble a bell curve with only 3 or 4?
Varsity gang✊✊✊
yess
His hand has a cat scratch on it! 😻
Spotting the oddest part of the video ! Good job !
Why is gravity ignored?
Guy from the discovery show!! 😍
Looking at the reddish scar, there is a good probability that he assembled the board just hours before he recorded this vid. Did it in a hurry and a nail scratched his hand..
amazing!!!!
From varsity🥳
Came here from ZERODHA Module (option trading) recommendation
Hey students of Canberra College ;)
+Khamis Buol ;)
+Khamis Buol inspirational comment, man you changed my life
+Khamis Buol
Bell curve right?
1:00 no, not "a few": only 1 end up in the end.
Yeah, this is right. Just because you have added more balls it hasn't changed the distribution :/ it just shows the shape better
Do you know where I can buy it?
you can make one
Pronounced "gall-ton" actually.
that's how he pronounced it
It's not the number of balls that match it to the normal distribution it is having more rows of pegs...
Who came here from zerodha varsity😃😃 do like
The Galton board doesn't show random distribution. You will always end up with a Bell curve.
From Zerodha varsity 😃
For more balls, better approximation of a normal distribution, so more balls = closer to the normal distribution curve. As for more pegs, its probably a similar story, but im not sure.
Hey ! 01:11 You could have cleaned that plastic funnel before shooting!
It is so easy
It called Galton board. It made by colorless balls. After that used a computer simulation program.
In details:
The process is done with all balls of white colour. After that, recording video for the balls are landed in each section at the bottom. Finally, effects of a computer colour simulation program is done for the recorded video.
You are funny. BTW someone did something like marble color sorting mechanical machine that turned out to be CGI trickery
Valve just disprooved the normal distribution, whoo'd a thunk
Interesting🤔 Next time when I play this game- I know how to win it? Thanks
Varsity brought me here
Varsity walo attendance lagao
is it just me or maybe its also just because of gravity? the balls are drawn towards the middle because its more likely to follow the downward path than the sideway path?
:DDDDDDDDDDd
The only time they move 'down' is after they have selected to go left or right. There is a 50% chance to go left or right each time. Gravity does not make a ball go left then right then left. Over 12 50% chances or left or right you would expect it to have gone left 50% and right 50% leaving it in the middle. Obviously with the way probability works this will never work out exactly, but more often than not the position will be towards the middle.
thanks stand up maths
can someone make a shader of this XD
No, not really.What if there was one peg and only two spaces for balls to drop into, would it look normal then? No, it would just be 50/50.
Adding more balls is showing how the "Law of large numbers" works which Bernoulli proved. Basically, this says that performing the experiment loads of times we will get close to the expected value. So the histogram of the walls will fit close to the actually distribution (whether it is normal or not)....
1:49 normal distribution? no way, that's binomial distribution
He did say binomial distribution tho
Parker distribution
Why is this unique? The funnel is dropped exactly in the center. For sure the middle will have more. Everything else is just a distraction.
ah okay, thanks very much
Hey ENGR 112 people!!
hello are the exams difficult
Wow
You mention the number of paths, but if it were a rectangular board extending infinitely to the sides, you would see the same pattern. The balls are clustering around the gravitational vector.
gravity direction ignored
This men is similar to France president
Zerodha varsity
Baka taga earist to HAHAHHAHAHAHAHHAHA
Ca-ra-le-o
just say Gaussian distribution
haha, your thinking is WRONG man :)