A239383 Decimal expansion of the probability of a normal-error variable exceeding the mean by more than two standard deviations.

2, 2, 7, 5, 0, 1, 3, 1, 9, 4, 8, 1, 7, 9, 2, 0, 7, 2, 0, 0, 2, 8, 2, 6, 3, 7, 1, 6, 6, 5, 3, 3, 4, 3, 7, 4, 7, 1, 7, 7, 6, 2, 2, 3, 7, 0, 1, 6, 7, 8, 4, 3, 3, 9, 8, 3, 6, 6, 6, 0, 0, 0, 1, 3, 0, 4, 7, 6, 2, 9, 0

Offset

-1,1

Comments

The probability P{(x-m)/s > 2} for a normally distributed random variable x with mean m and standard deviation s. In experimental sciences (hypothesis testing), a measured excursion exceeding background "noise" by more than two standard deviations is considered mildly significant if corroborated by additional indications.

Links

Stanislav Sykora, Table of n, a(n) for n = -1..1999

Wikipedia, Normal distribution

Formula

P{(x-m)/s > 2} = P{(x-m)/s < -2} = 0.5*erfc(2/sqrt(2)) = erfc(sqrt(2))/2, with erfc(x) being the complementary error function.

Example

0.0227501319481792072002826371665334374717762237016784339836660...

Mathematica

First[RealDigits[1 - CDF[NormalDistribution[], 2], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)

Prog

(PARI) n=2; a=0.5*erfc(n/sqrt(2))  \\ Use sufficient realprecision

Crossrefs

Cf. P{(x-m)/s>n}: A239382 (n=1), A239384 (n=3), A239385 (n=4), A239386 (n=5), A239387 (n=6).

Sequence in context: A277199 A116077 A074144 * A325525 A309554 A011146

Adjacent sequences: A239380 A239381 A239382 * A239384 A239385 A239386

Keyword

nonn,cons

Author

Stanislav Sykora, Mar 17 2014

Status

approved