Have never had anyone in my entire student career that explained math with such clarity and passion. I have been seeing this entire video at half past midnight and this felt interesting, not frustrating!
Never in all my life, has a teacher explained mathematics in this way. The "adding" of different rules to augment the behaviour of the graph is so helpful for students who want to understand the REASON for the behaviour.
If only I had a teacher like Eddie Woo, I would have certainly taken Maths as my honours. When I first looked at the PDF of normal distribution, I fainted thinking its only people at PhD maths level could decipher. Now it makes sense how it came into picture so easily. I am a huge fan of Eddie😊
The Normal distribution equation was really daunting at first but you really clarified and derived well and simplified things a whole lot more. Thank you so much.
13:08, Sir Eddie said, it is not an exclamation sign but a mathematical notation, okay! It's called Factorial. I laughed so goddamn hard! You are really AN AMAZING TEACHER! LOVE YOU MAN!
Eddie - At 1:25 you eliminate trigonometric functions (no horizontal asymptote), but arctan(x) has a horizontal asymptote. Graph the function pi/2-arctan(x^2) and you get something that looks remarkably similar to the normal distribution. If you include a dilation of 1/(pi.root(2)) the function has a definite integral of 1 over the domain (-infinity, + infinity). Now you will need to graph it against the "normal" distribution to see that it is actually different. Now consider the graph of 1/n - 1/n tanh(x^2/n) and you get something even better. Of course this might be thought of as cheating since the tanh(x) is related to e^x ... and hence why we cannot eliminate trigonometric functions from the mix so easily.
U R a good teacher. U explain it such that I can UNDERSTAND it, not replicate it from memory. With such knowledge, I can derive usage of this in other theoretical applications. Most people memorize, but I don’t ever remember it unless I UNDERSTAND its applicability. Thanks. I want to learn more about the CDF and how you arrive at it using the PDF. I think you’re going to use an area under the curve, but am not sure.
I just don't have words to express how exceptional your style of teaching is... Never had a teacher this passionate who sort of untangles all the complicated stuff step by step in an orderly way so that students can actually understand the concept. Thank you so much sir! I really really appreciate the effort you put in.. 🙏🏻🙏🏻 You might never see this but I just couldn't help but say it 🥰🥰
wow is incredible how much out educational systems differs each other, I know what a factorial is but I have never studied the normal distribution... thanks!!
WOAH this was explained beautifully. I've never had anyone derive the normal distribution function like that, it actually makes so much sense :o By the way, I have to wonder... What level of math does he teach? Because he's explaining rather difficult topics such as z-scores, PDFs, and integration, but his students don't know what a factorial is? Pretty interesting to say the least
AFAIK these are 12th grade high school students. I was also weirded out by the fact that some of his videos are explaining elementary school stuff, like area of a triangle, then comes this... :D
He is a high school teacher. He teaches 2u (advance) math for year 12 this year in NSW. He also teaches from year 7 to year 12 like other high math school teachers do. I’m a current year 12 student. But I actually wonder how his school allows him to teach 2u instead of 4u math. He is a fantastical teacher!!!
He did a little bit of math misdirection there: he made you pay attention to exponential functions, when really a lot more going on --- but he swept the other details under the rug. Like what about y = 1/(1+x^2)? There's a rational function with no vertical asymptotes, and its graph looks just like the normal distribution. He didn't explain why statisticians don't use this function instead of exponential (hint: integrals). He glossed too quick over the rational functions, but yes it was convincing if you're not looking closely :)
That wasn't a derivation. It's just simplification. He doesn't even tell what the 2pi is there for. It's a shame. Advanced students could use an excellent teacher too, not just high school kids.
If you're watching this and are interested in knowing where the cumulative distribution function comes from, it's the integral of the Maclaurin series expansion of e^-1/2z^2 centred at z=0. Don't know what that means? Google search or search on UA-cam "Maclaurin series" and it'll make a lot more sense why it looks the way it does.
I prefer the term Taylor Series, because it is a polynomial that is TAILORED to match the behavior of the function, by matching every order of derivative at one point.
I regret I did not major in maths. Nevertheless I enjoy learning all these stuffs now. But I can guarantee if he had been my teacher, I would have choose a math track for sure.
The sqrt(2*pi) and sigma^2 come from "forcing" the function to have a total area under the curve of 1, since a probability density function must have a total integral of 1 for it to make sense for the application. If you integrate e^(-x^2) dx over all real numbers, which is called the Gaussian function, you will end up with sqrt(pi). To do this, you make a coordinate transform by squaring the function, and carrying out the integral in polar coordinates. You will integrate e^(-r^2)*r*dr*dtheta from r=0 to infinity, and theta = 0 to 2*pi. Doing this, allows us to perform integration by substitution, to make sense of this function that can't be integrated in closed-form. The variables of integration switch from dx * dy to r*dr*dtheta, and the r in this term becomes just what our integration method was asking for, so it could be possible to solve. This works well for finding the grand total area, but unfortunately, intermediate ranges cannot be integrated in closed form. We end up using a Taylor series of this function to define erf(x) and erfc(x) as the integral of it, so the distribution function can be integrated. In order for it to have a standard deviation equal to 1, when sigma is set to 1, we make another adjustment to the coefficient. Carry out the calculus that determines the variance on (1/sqrt(pi))*e^(-x^2), and we end up with a variance of 1/2, implying a standard deviation of 1/sqrt(2). To correct for this, sqrt(2) gets inserted into the denominator, and 1/2 gets inserted into the exponent. This gives us the standard normal in the form of: 1/(sqrt(2*pi) * e^(-1/2*x^2) When we want to shift it laterally so it is centered on mu, we replace x with (x - mu). When we want to scale it laterally by sigma, we replace (x - mu) with (x - mu)/sigma. We then put sigma^2 in the denominator of the coefficient out in front, to "force" the area to equal 1.
Why show the antiderivative of a function without an elementary antiderivative, using the Maclaurin series, to kids who have no idea what the Maclaurin series is...or, for that matter, the factorial
Do you share your slides somewhere? I’m a tutor helping students that have trouble with math and I would love to explain concepts using your slides. Thanks for making learning fun, you are the cornerstone of society!
Hey, can someone help me start the stats videos? I don't really know where to begin. I really love your videos and I watched the whole complex number playlist, now I want to watch the statistics one, but I don't know where to start.
ua-cam.com/play/PL5KkMZvBpo5C9nhzyacvNtcWHLh3mvXJE.html This should take you to where most of the probability/statistics videos should be. The topics are sorta all over the place video to video, so I really recommend watching these as a supplement to a Stat class. This playlist could be useful to you also ua-cam.com/play/PL5KkMZvBpo5Bcz-V51UHtlg_eBW-PtQ7_.html
This comment is directed at Mr Woo, because of his comment on the importance of this function. But anyone interested in metaphysics is welcome to respond. Is the law of averages the most powerful force in the universe? This is a serious question - one which lead me to a simple explanation of several hitherto unexplained phenomena - such as the resistant idea of a God.
My take on the matter is that we find such patterns because our psychology evolved in such way, we’re not even sure if other intelligent life somewhere else in the universe possesses said abilities. Also, regardless of whether they’re intrinsic to the fundamental framework of the universe or not, invoking god here is an argument from ignorance which is a logical fallacy.
Have never had anyone in my entire student career that explained math with such clarity and passion. I have been seeing this entire video at half past midnight and this felt interesting, not frustrating!
OMG me too!
Amen!
Never in all my life, has a teacher explained mathematics in this way. The "adding" of different rules to augment the behaviour of the graph is so helpful for students who want to understand the REASON for the behaviour.
I agree with you, sir. This was quite illustrative to watch.
If only I had a teacher like Eddie Woo, I would have certainly taken Maths as my honours. When I first looked at the PDF of normal distribution, I fainted thinking its only people at PhD maths level could decipher. Now it makes sense how it came into picture so easily. I am a huge fan of Eddie😊
me too
OMG!!! such a neat and crisp explanation!! Thanks sir!
The Normal distribution equation was really daunting at first but you really clarified and derived well and simplified things a whole lot more. Thank you so much.
13:08, Sir Eddie said, it is not an exclamation sign but a mathematical notation, okay! It's called Factorial.
I laughed so goddamn hard! You are really AN AMAZING TEACHER! LOVE YOU MAN!
Eddie - At 1:25 you eliminate trigonometric functions (no horizontal asymptote), but arctan(x) has a horizontal asymptote. Graph the function pi/2-arctan(x^2) and you get something that looks remarkably similar to the normal distribution. If you include a dilation of 1/(pi.root(2)) the function has a definite integral of 1 over the domain (-infinity, + infinity). Now you will need to graph it against the "normal" distribution to see that it is actually different.
Now consider the graph of 1/n - 1/n tanh(x^2/n) and you get something even better. Of course this might be thought of as cheating since the tanh(x) is related to e^x ... and hence why we cannot eliminate trigonometric functions from the mix so easily.
Omg I have an applied test this week and this just came in clutch. Tsym Eddie.
You Aussies are very lucky to have a teacher like Eddie Woo
U R a good teacher. U explain it such that I can UNDERSTAND it, not replicate it from memory. With such knowledge, I can derive usage of this in other theoretical applications. Most people memorize, but I don’t ever remember it unless I UNDERSTAND its applicability. Thanks. I want to learn more about the CDF and how you arrive at it using the PDF. I think you’re going to use an area under the curve, but am not sure.
I just don't have words to express how exceptional your style of teaching is... Never had a teacher this passionate who sort of untangles all the complicated stuff step by step in an orderly way so that students can actually understand the concept. Thank you so much sir! I really really appreciate the effort you put in.. 🙏🏻🙏🏻 You might never see this but I just couldn't help but say it 🥰🥰
Hands down the best teacher ever :)
wow is incredible how much out educational systems differs each other, I know what a factorial is but I have never studied the normal distribution... thanks!!
I feel lucky I came across Woos content, this is just a life saviour. So simple.
OMG wow! I never in my life knew that this could be traced down in this way. Thank you so much.
I wish i had any teacher like you in my life. How passionate seem.
Its really blew my mind, you made Gaussian standard distribution something easy to understend, thats the thing, thx!
the best teacher ever, you earned a new subscriber. wow, I am super impressed
Honestly Eddie you explain everything so well
I wish I had teachers like him. These kids are literally so lucky
this men is a legend!
I LOVED EVERY SECOND OF THIS!!!!
Perfect way to do my revision as I prepare for end of semester exam... inspirational
One of the best math videos on youtube hands down 🔥
Man, you are a great teacher.
The way he explained it is so good!
i wish i had a teacher like u! u made me so interested in this!
I love this teacher even though I'm not a student anymore (I'm 32 but still trying to better visualize what I already know).
just wow, wonderful video. Thank you!
Seriously dude, I really appreciate your videos. I like your teaching style and way of communicating things. Keep up the good work! Cheers.
WOAH this was explained beautifully. I've never had anyone derive the normal distribution function like that, it actually makes so much sense :o
By the way, I have to wonder... What level of math does he teach? Because he's explaining rather difficult topics such as z-scores, PDFs, and integration, but his students don't know what a factorial is? Pretty interesting to say the least
AFAIK these are 12th grade high school students.
I was also weirded out by the fact that some of his videos are explaining elementary school stuff, like area of a triangle, then comes this... :D
He is a high school teacher. He teaches 2u (advance) math for year 12 this year in NSW. He also teaches from year 7 to year 12 like other high math school teachers do. I’m a current year 12 student. But I actually wonder how his school allows him to teach 2u instead of 4u math. He is a fantastical teacher!!!
He did a little bit of math misdirection there: he made you pay attention to exponential functions, when really a lot more going on --- but he swept the other details under the rug.
Like what about y = 1/(1+x^2)? There's a rational function with no vertical asymptotes, and its graph looks just like the normal distribution. He didn't explain why statisticians don't use this function instead of exponential (hint: integrals). He glossed too quick over the rational functions, but yes it was convincing if you're not looking closely :)
That wasn't a derivation. It's just simplification. He doesn't even tell what the 2pi is there for. It's a shame. Advanced students could use an excellent teacher too, not just high school kids.
@@biubiu9356 What do you mean by "2u" and "4u"?
This professor is top class.
I can't believe Iam watching all his fantastic explanations for long hours he is best
You are best because of you my interest and love for maths is growing it's getting stronger and probably physics also becoming strong thanks a lot
Thanks Eddie.. one of the best explanations I found.
I was so impressed! Great job Eddie! It would've been nicer if the students could keep quiet for a while! Great job!
What is the next part of this video? Jesus! this is so good! Thanks, Prof. Woo
You are a genius. Thanks.
If you're watching this and are interested in knowing where the cumulative distribution function comes from, it's the integral of the Maclaurin series expansion of e^-1/2z^2 centred at z=0. Don't know what that means? Google search or search on UA-cam "Maclaurin series" and it'll make a lot more sense why it looks the way it does.
I prefer the term Taylor Series, because it is a polynomial that is TAILORED to match the behavior of the function, by matching every order of derivative at one point.
Just Beautiful and WOW
Very lively class💞✨
Best explaination of PDF
That's an outstanding explanation
wonderful teaching! wish i had you as my statistics teacher
An active class🙌👏👏
Love this!
thank you for your efforts
Very clear, thank you so much.
This is wholesome
saving my life atm
Damn, now I'm gonna remember this equation forever!
These kids are the luckiest people on earth. If he was my Math teacher i would have become a Mathematician
wish i had a teacher like him
what kind of class is there where they know what integrals are but don't know what factorials are?
Ye no clue im sitting the same syllabus as them and i cant believe they dont know
At lest one person didn't. conclude nothing on sample sizes of one!
In Australia integrals are a part of the advanced course but factorials are only done in extension :)
yh I was confused too lol.
i think the class is staged.
Thank you
Amazing!! THANK YOU!
the best part of this vedio is when eddie brings the upside down parabola onto the screen & everyone is awestruck,,is pretty good right😍
I regret I did not major in maths. Nevertheless I enjoy learning all these stuffs now. But I can guarantee if he had been my teacher, I would have choose a math track for sure.
professor eddie woo is so underrated
Mesmerising. Thank you very much sir for lucid explanation. Would you please explain about the coefficient (1/sigma^2. Sort (2pi). How did we get it
yes, please
The sqrt(2*pi) and sigma^2 come from "forcing" the function to have a total area under the curve of 1, since a probability density function must have a total integral of 1 for it to make sense for the application.
If you integrate e^(-x^2) dx over all real numbers, which is called the Gaussian function, you will end up with sqrt(pi). To do this, you make a coordinate transform by squaring the function, and carrying out the integral in polar coordinates. You will integrate e^(-r^2)*r*dr*dtheta from r=0 to infinity, and theta = 0 to 2*pi. Doing this, allows us to perform integration by substitution, to make sense of this function that can't be integrated in closed-form. The variables of integration switch from dx * dy to r*dr*dtheta, and the r in this term becomes just what our integration method was asking for, so it could be possible to solve. This works well for finding the grand total area, but unfortunately, intermediate ranges cannot be integrated in closed form. We end up using a Taylor series of this function to define erf(x) and erfc(x) as the integral of it, so the distribution function can be integrated.
In order for it to have a standard deviation equal to 1, when sigma is set to 1, we make another adjustment to the coefficient. Carry out the calculus that determines the variance on (1/sqrt(pi))*e^(-x^2), and we end up with a variance of 1/2, implying a standard deviation of 1/sqrt(2). To correct for this, sqrt(2) gets inserted into the denominator, and 1/2 gets inserted into the exponent.
This gives us the standard normal in the form of:
1/(sqrt(2*pi) * e^(-1/2*x^2)
When we want to shift it laterally so it is centered on mu, we replace x with (x - mu).
When we want to scale it laterally by sigma, we replace (x - mu) with (x - mu)/sigma.
We then put sigma^2 in the denominator of the coefficient out in front, to "force" the area to equal 1.
damn i wanna know what happens on Thursday and Friday where's the video for that Mr Woo
Great
brilliant
well done
If he was my instructor i'd study math major for sure
Why show the antiderivative of a function without an elementary antiderivative, using the Maclaurin series, to kids who have no idea what the Maclaurin series is...or, for that matter, the factorial
4 dislikes? I see.... Do those guys have functional eyes? or ears? I mean, Eddie Woo, you could only solve this puzzle :D
can somebody explain why not Rational Functions?
suppose a rational function whose denominator is non zero like 1/(1+x^2)
please help
Integrals are easier to compute with exponentials, that’s why.
Do you share your slides somewhere? I’m a tutor helping students that have trouble with math and I would love to explain concepts using your slides. Thanks for making learning fun, you are the cornerstone of society!
6:16 shildnt mean as a plus?
Hey, can someone help me start the stats videos? I don't really know where to begin. I really love your videos and I watched the whole complex number playlist, now I want to watch the statistics one, but I don't know where to start.
ua-cam.com/play/PL5KkMZvBpo5C9nhzyacvNtcWHLh3mvXJE.html This should take you to where most of the probability/statistics videos should be. The topics are sorta all over the place video to video, so I really recommend watching these as a supplement to a Stat class.
This playlist could be useful to you also ua-cam.com/play/PL5KkMZvBpo5Bcz-V51UHtlg_eBW-PtQ7_.html
So that's where the Gaussian function comes from. I thought it was from Hell. Neener to Demons!
Anyone know where he teaches?
Sydney, Australia
@@dhruvsingh34 can you tell in which grade these students are??
@@morancium No Idea, Ashish.
But he teaches at some High School.
Check *About* of his UA-cam Channel.
@@morancium year 12 im in yr 12 and we have to learn this
They are talking so loud during the lec. He has some real patience while teaching.
Where
Damn
This comment is directed at Mr Woo, because of his comment on the importance of this function. But anyone interested in metaphysics is welcome to respond.
Is the law of averages the most powerful force in the universe? This is a serious question - one which lead me to a simple explanation of several hitherto unexplained phenomena - such as the resistant idea of a God.
My take on the matter is that we find such patterns because our psychology evolved in such way, we’re not even sure if other intelligent life somewhere else in the universe possesses said abilities. Also, regardless of whether they’re intrinsic to the fundamental framework of the universe or not, invoking god here is an argument from ignorance which is a logical fallacy.
@@randomblueguy Colossians 2:3 IN Christ (GOD) are hidden all the treasures of Sophia(wisdom) and gnosis(Knowledge).
POV: HSC is tmr
Guys are studying normal distribution and don't know about factorials, I mean really??
lol ya trueee
I mean...the class does know that the video will end up on UA-cam. Can't they just co-operate to save themselves some nasty judgment.
relax dude.
8:11 PAUSE.... I was like whaaaaaat he say?
MY daughter?