Normal distribution's probability density function derived in 5min

The proof comes from Grossman, Stanley, I., Multivariable Calculus, Linear Algebra, and Differential Equations, 2nd., Academic Press, 1986., and Hamming, Richard, W. The Art of Probability for Engineers and Scientists, Addison-Wesley, 1991. This was summarized by Dan Teague of the North Carolina School of Science and Mathematics. This did not use characteristic functions or moment generating function to derive, because this explanation was straightforward. A disclaimer is that, in the second step, the improper integral appears without proper treatment that this is allowed. However, digging into the details of this would be beyond the scope for this video made to make the content simple.

[davidgol]

Although I had to pause several times, this video's content is A++. My only critique is that there really isn't a need to "rush" so much.

[hhehe]

Extremely dense and nutritious in information. I also greatly appreaciate the sources. Hard to grasp but that is just due to the topic at hand. Good video!

[梦烦啦]

It's worth noting that, since g(r) is independent of the angle (as mentioned earlier in the video), d(g(r))/d(theta)=0 because the change in angle should not result in the change in probability, only area and position matters, therefore derivative is zero because the change in probability resulted from the change in theta is zero.

[АндрейОнищенко-зх]

It is so fast that impossible to watch without pausing lots of times but the content is actually really good and exactly what I was looking for. Nice job! And thank you!

[mathteacher]

I was clue-less on how to begin that derivation.
Now I have a starting point.  I like how you broke it down into three pieces.
All in all, in my opinion it was excellent!

[esreve]

I had to see the video several times to understand the derivation. Afterwards I looked again just for the pleasure of seeing something so well done. Thanks!

[stevenshropshire]

This video is one of the very best I have ever found. If you do a little living in between viewings, it gets better every time you come back to it.

[deltaexplorer]

I have been searching for this explanation for a long time !!  THANK YOU, THANK YOU, THANK YOU VERY MUCH.

[Zenoandturtle]

I once asked my lecturer who could not explain it! Thanks!

[DarjoScn]

Man thank you, I just wish it wasn't so fast!

[superlinux]

This took me like hours to decipher and decompress the information in it. many rules and many steps have been taken for granted and were skipped.

[hydraslair]

Amazing derivation. This argument makes way more sense than the usual ones I've seen (the ones about independence of x and y in throwing darts).

[CommanderSpky]

Pretty good video that serves my imparience! Surely, I'd love a slightly more detailed proof but I'm very satisfied with this and learned more in 5 minutes that I could in 15. Thank you!

[dawarfarooq]

This is one of the most beautiful videos I have ever seen. I cried at one point in this video.

[RealationGames]

Way too fast to grasp any new info.
This is good for revision, but way too fast to learn.

[sgdrifter]

you did it in 5 mins, but ppl lost in 5 sec.

[winstonvan]

This is the perfect speed imo. I'd rather pause and learn at my own speed than wait for a 17 min video to get to the part I need to learn. Thanks!

[santiagomorales]

Thank you so much, i had been looking for this for a long time.

[supreethmsv]

Brilliant way of explaining ! before seeing this video I had no idea what a Guassian function is ! now i can explain others what is is ! thanks a ton for the video

[MisterF_]

This is an excellent video, everything summed up concisely and quickly with minimum pandering and no getting sidetracked.