# Probability Integral

## Probability Integral

the name of several mutually related special functions. The integral

is called the Gaussian probability integral. For a random quantity *X* having a normal distribution with an expected value 0 and variance σ^{2}, the probability of the inequality ǀ*X*ǀ ≤ *x* is equal to Φ(*x*/≤. In addition to this, the name “probability integral” is used for the integrals

The latter function is usually designated erf (*x*) (from “error function”).

### REFERENCE

Bol’shev, L. N., and N.V. Smirnov.*Tablitsy matematicheskoi statistiki*. Moscow, 1965.