Deriving the Normal Distribution Probability Density Function Formula

[vikramanbaburaj]

Will be helpful for those want to know deep about the topic.

[whistlinghouse]

Excellent explanation. Great job. I am particularly impressed that you explained even the minutest details. Thanks. Can you post similar videos for other distributions as well. For example, Beta, Weibull, Poison etc.

[marcushendriksen]

Great video! I particularly liked how you took the time to highlight the relationship between lambda and the spread.

[jeevanjose]

Brilliant explanation! Love how you took care of any questions we would potentially in between the steps. Subscribed! 🙏

[IntegerFactoring]

So I’ve seen two comments wondering about why g(x) is set to K*exp(kx^2). So I’ll explain why. If you use the substitutions:
h(z) = log(g(sqrt(z)))
u = x^2
v= y^2

You get h(u+v) = h(u) + h(v)
Where h(w) = aw+b are a class of functions that satisfy the property.
If I remember correctly, there are other classes of functions that satisfy this property, but they are weird, I think pathological if I recall correctly, which I guess aren’t as “nice” as linear functions.

[kamranabbas]

Excellent video, especially when you piece it together with derivation of the Gaussian Integral. Thank you very much!

[xaqaniqasimov]

Thank you very much, perfect explanation, and now I can feel comfortable...

[johannaw]

Helpful. Thank you for going through every step.

[manikandank]

Excellent explanation Sir👏👏, thank you

[akilanramesh]

Haven't seen any video or full proper explanation about this derivation, from a student in need for his school main project thanks alot and im definitely sourcing you for my project(don't worry lol).

[Rondon]

thank you so much. i remember watching this a while ago and now I needed it. happy you had it on youtube still.

I'll prefer to fix k = -1 first to make the derivation easier. it follows sigma^2 = 1/2. and from that we can apply lineartransformations.

[abdul-kadersouid]

Outstanding, clear and precise. How about if you add examples to the use of the CDF? With many thanks and appreciations

[wqltr]

I wonder if there are variants of the normal distribution, by this I mean continious functions who satisfy the original assumptions and ehen integrated from neg inf to pos inf equals one.

This could be explored by taking the line g(x)g(y)=g(sqrt(x^2 + y^2)) and trying to find other solutions for g. Or maybe it can be proved the only a certain family kf functions exist, idk.

[xaxion_faza]

A very elegant video. A quick question, why does w(r) = f(x).f(y) ?

[onepunchman]

Do you multiply f(x) with f(y) because you want to express AND?

[vedantjhawar]

Quick question. After rewriting the function based on f(y) where y=0 is a constant, everything else flows smoothly. I dont understand, however, how y itself can be regarded as static without the derivation restricting calculations of other y-values. Do let me know if you would like me to clarify my question. Thank you.

[Meatbrick]

Safe to say I couldnt understand anything past 9:00. Could you leave a trail of references and math topics that a student could look into to better understand?

[pjakobsen]

What is the symbol you call "ORR" or "OHR" that looks like an r? Is this a greek letter ?

[chengchuanliu]

Fantastic Video!!! I love the way you make the explanation! A quick question at 31:10 I don't quite understand why you consider x goes to infinity and the red-circle-part becomes null. Surely if we plug in 0, it is 0 as well. But if we plug in 1, it has value not equal to 0. Thanks!

[harekrishnapradhan]

I couldn't understand
If w(x)=lambda.f(x) only when y=0 then after that all the steps involving y are just identities like 1=1
Explain?