I used this method specifically to prove the 68.2% 95.4% and 99.7% of the population under a gaussian within 1,2 and 3 standard deviations respectively, although a taylor expansion solution isn't as nice as an elementary function since it's hard to do things like solve for a value or find the inverse function for example
Yeah but this is, just as you said, an approximation. Besides you can evaluate the integral in the video from 0 to 1 with the same method as the gaussian integral because both are converging to a finite value over the limits of integration. You can take I as the integral from -1 to 1 of e^x² and since e^x² is an even function, your target integral will be I/2. Then you can use any of the methods used to solve the gaussian just with the limits being -1 to 1 instead of -infinity to infinity
What method did you use to approximate the integral?
No worries just define the error function as the solution to this integral 😂
Hahahahaha
NGL I thought this was gonna be a 1 min prank vid and that he was gonna do exactly this 😄
@@numbers93 lol
how would you approximate the gaussian integral after this? i tried but im not sure
I used this method specifically to prove the 68.2% 95.4% and 99.7% of the population under a gaussian within 1,2 and 3 standard deviations respectively, although a taylor expansion solution isn't as nice as an elementary function since it's hard to do things like solve for a value or find the inverse function for example
Oh that’s epic! I’ve never used this in a statistical application
@@NumberNinjaDave well when i had to i had no choice but to use it, and there we go
Yeah but this is, just as you said, an approximation. Besides you can evaluate the integral in the video from 0 to 1 with the same method as the gaussian integral because both are converging to a finite value over the limits of integration. You can take I as the integral from -1 to 1 of e^x² and since e^x² is an even function, your target integral will be I/2. Then you can use any of the methods used to solve the gaussian just with the limits being -1 to 1 instead of -infinity to infinity
Very true, 🥷