actually tumbs up hold a rlly important value, its like money, it only holds value cause we want it to hold it, same here
thumbs up are valuable cause we give them as a simbol of aproval
"the impossible integral" - given you're integrating with respect to x. Normal distribution is tabulated, but despite that the exact answer exists (the 1st theorem of calculus or something), we cannot express it. Not even with Fourier integrals!
But i can tell you that if you integrate from -sigma to +sigma, you get about 68% of the whole integral, if you double the limits you're up to 95%, and +-3sigma gives 99,7% of the total value of the integral, for any given mean & standard deviation.
From ?
To ?
From what i took in Probabilities i think that is the density function of the normal law N(Î¼;ÏƒÂ²) which we didn't integrate (2complex4me) so you just reduce it to N(0;1) and use a table.
Since we're integrating a normalized form of a Gaussian function, we'll have an error function defined by: erf(z)=2/âˆš(pi/2) * integral of e^(-t^2) dt from 0 to z
eventually, we get (Î´/2) Erf((x-Î¼)/((âˆš2)Î´) + c