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In class it was claimed that Gaussian probabilities cannot be found analytically with a definite integral...

In class it was claimed that Gaussian probabilities cannot be found analytically with a definite integral of the Gaussian PDF. Change my mind with a Gaussian DEFINITE integral.

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Let X be a R.V. having Normal Distribution .

X\sim N(\mu,\sigma^2)

XN Uhe is pelf fata) e ) 1 くえ det Drample Jake us Suspose pebabiliy N 4) we tue want compute gkeates to is that tHhan Pl x) 1-O.5 dy e y 1 JTT Jluis givers is ganmma-integral by e ax x (of-1) ey duy 0.5-1 PCX2) o.5 1 o.5 TT 1 o.5 PC X ) O.5 1 LOThus , the Gaussian Probabilities can be found by integrating the Gaussian PDF . But , this integral could be messy and time consuming . So , we generally prefer Standard Normal Distribution Tables to compute the Gaussian Probabilities

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