Proof: Integral of PDF of Normal Distribution is Equal to 1 (in English)

This video shows how to prove that the Integral of PDF of Normal Distribution from negative infinity to positive infinity is Equal to 1 explained in English.
References:
Evaluation of Integral of e^(-x^2) or the Gaussian Integral: • Integral of e^(-x^2). ...
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[@sagessendulani]

You save my life with this video. Thank you very much

[@halimamotee9247]

Extremely helpful, thanks

[@churunlmaknun2501]

Thank you, it helps a lot

[@andorLOLChannel]

Very explanation and understandable helpful!

[@muhamadrifai3216]

Thanks for the proof, Sir!

[@subharthipradhan5987]

Sir, can you provide table value through pdf manually????

[@TGSG-rb5hz]

God bless you

[@융융-o3k]

Thanks! I perfectly understand👍

[@saqihere]

Thank

[@tomgreen5736]

when you take the square root of z^2 shouldn't it be abs(z)? Is there some way you know z is always positive?

[@computationempire8603]

If you are referring to y^2 = z^2/2. I'm showing that to show my objective of simplification. I can either use y = z/sqrt(2) or y = -z/sqrt(2) as solutions to that equation. So y can either be positive or negative. For the first one, it results in the integral limits of from -infty to +infinity since as z -> infinty, y -> infinty (and also with negative infty). For the second one, it results in the integral limits of from +infinity to -infinity but dy will be negative. It should result in the same answer. So in conclusion, you can choose either y=z/sqrt(2) or y =-z/sqrt(2). Just the first one is simpler.

[@ymstatistics2023]

👏👏

[@owusualfredkwabena8929]

Thanks Sir

[@zhangshijia1752]

Hello, I am a little confused about the basics, why -(sigma * Z)^2 = -sigma^2 * Z^2

[@MikaelSepaul]

Look: -(a * b)^2 = - [ (a)^2 * (b)^2] The negative sign is applied to both factors. So, like the exponential to the second power, since both are in the same parenthesis, each of the items in the parenthesis is squared first and then the negative sign is changed.

[@dancus25]

a jövőkor figyelmébe: ennek a videónak a kibővített verzióját elfogadja Soós néni