Talk:Vysochanskiï-Petunin inequality

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I know about the policy Wikipedia:No original research, but it might be worth stating that I believe this result can be improved to:

P(\left|X-\mu\right|\geq \lambda\sigma)\leq\frac{4}{9\lambda^2}
when \lambda \geq 1.38539...
 
P(\left|X-\mu\right|\geq \lambda\sigma)\leq 1-\left({4 \lambda^2 \over 3(1+\lambda^2)}\right)^2
when \lambda \leq 1.38539...
 
where 1.38539... = \sqrt{{2 \over 3}+ \sqrt{124 \over 63}\cos \left( {\cos^{-1}\left( \sqrt{847 \over 29791} \right) \over 3} \right)}

--Henrygb 01:31, 16 Aug 2004 (UTC)