# 3.5.3.1.21 Prob

## Definition:

The prob(x) function is the Probability Density (for a normal distribution) integrated from $-x$ to $+x$.

It has the limiting values $prob(0)=0$, and $prob(\infty )=1$. Mathematically:
$Prob(x)=\frac 1{\sqrt{2\pi }}\int_{-x}^{+x}e^{\frac{-t^2}2}dt$

Note that $prob(-x) = -prob(x)$, $prob(x)= erf(\frac x{\sqrt{2}})$ or $prob(x) = 2 * Normal Distribution Function -1$.