Gaussian Definite Integral Problem?
Would a Gaussian definite integral be able to be used to find Gaussian probabilities?
"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."
- az_lenderLv 72 months agoFavorite Answer
Values of the Gaussian definite integral at finely resolved abscissa values have been calculated to a great many digits, by numerical methods such as approximations by infinite series. These values are tabulated and widely available.
"Cannot be found analytically" usually means you can't represent the answers in terms of "elementary" functions such as algebraic, trigonometric, exponential, or logarithmic functions.
- nbsaleLv 62 months ago
I think the answer is that these integrals cannot be expressed in terms of elementary functions. The value of the definite integral must be found using some kind of numerical technique or approximation. So THE Gaussian probability can't generally be found as an exact expression.