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A239383 Decimal expansion of the probability of a normal-error variable exceeding the mean by more than two standard deviations. 8
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 (list; constant; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Mar 17 2014
STATUS
approved

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Last modified February 28 19:33 EST 2024. Contains 370400 sequences. (Running on oeis4.)