OMG me too!

Amen!

I agree with you, sir. This was quite illustrative to watch.

me too

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.

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.

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"?

kzfaq.info/sun/PL5KkMZvBpo5C9nhzyacvNtcWHLh3mvXJE 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 kzfaq.info/sun/PL5KkMZvBpo5Bcz-V51UHtlg_eBW-PtQ7_

Integrals are easier to compute with exponentials, that’s why.

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.

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 KZfaq Channel.

@@morancium year 12 im in yr 12 and we have to learn this

Where

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).

relax dude.

lol ya trueee