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3.5.3.1.24 Prob
Definition:
The prob(x) function is the Probability Density (for a normal distribution) integrated from /math-d25c186e3f3096a9ff4a918f7b3141d4.png?v=0 "-x")
to /math-34128bbb7914f13de6b658dd4e6a5855.png?v=0 "+x")
.
It has the limiting values /math-b0c87ea6bdb74e6a115866cbd99edeef.png?v=0 "prob(0)=0")
, and /math-f8f85653ef42bfe5b0d3ea0923b7a56e.png?v=0 "prob(\infty )=1")
. Mathematically:
/math-1395f04caa85b6532adbb3dff8ee8b68.png?v=0 "Prob(x)=\frac 1{\sqrt{2\pi }}\int_{-x}^{+x}e^{\frac{-t^2}2}dt")
Note that /math-92327bc0a82ed2f7173e6f23cc9948a4.png?v=0 "prob(-x) = -prob(x)")
, /math-96ed92100ab666b0f1c84f16a4faa432.png?v=0 "prob(x)= erf(\frac x{\sqrt{2}})")
or /math-7402b7bc06c0dedfcd2210fdad68ae60.png?v=0 "prob(x) = 2 * Normal Distribution Function -1")
.