The probabilistic nature of Wallis's formula

The probabilistic nature of Wallis's formula

The beautiful representation of π by Wallis's product formula has attracted many authors who have given a variety of proofs (see [1, 2, 3, 4, 5, 6, 7]). The purpose of this note is to revisit some elementary derivations with a focus on probabilistic/statistical flavours of this formula. The fam...

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Veröffentlicht in:Mathematical gazette 2012-07, Vol.96 (536), p.193-200
1. Verfasser: KHAN, RASUL A.
Format: Artikel
Sprache:eng
Schlagworte:
Cauchy Schwarz inequality
Density distributions
Gaussian distributions
Logical proofs
Mathematical inequalities
Mathematical integrals
Random variables
Statistics
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Zusammenfassung:The beautiful representation of π by Wallis's product formula has attracted many authors who have given a variety of proofs (see [1, 2, 3, 4, 5, 6, 7]). The purpose of this note is to revisit some elementary derivations with a focus on probabilistic/statistical flavours of this formula. The famous Wallis's product formula for is given by There are a number proofs available for this formula scattered in the literature. Here we will concentrate on the probabilistic nature of this formula.
ISSN:0025-5572
2056-6328
DOI:10.1017/S0025557200004411