Difference between revisions of "Delta Tschebycheff inequality"

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==Theorem==
 
Let $\mathbb{T}$ be a [[time scale]] and let $\epsilon > 0$. Then
 
Let $\mathbb{T}$ be a [[time scale]] and let $\epsilon > 0$. Then
 
$$\dfrac{\mathbb{V}ar_{\mathbb{T}}(X) - \mathbb{E}_{\mathbb{T}}(2H(X))}{\epsilon^2} \geq P((X-\mathbb{E}_{\mathbb{T}}(X))^2 \geq \epsilon^2),$$
 
$$\dfrac{\mathbb{V}ar_{\mathbb{T}}(X) - \mathbb{E}_{\mathbb{T}}(2H(X))}{\epsilon^2} \geq P((X-\mathbb{E}_{\mathbb{T}}(X))^2 \geq \epsilon^2),$$
 
where the density function of $H(X)$ is $h_2(t,0)-\dfrac{t^2}{2}$.
 
where the density function of $H(X)$ is $h_2(t,0)-\dfrac{t^2}{2}$.
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==Proof==
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==References==
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{{:Delta inequalities footer}}
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest revision as of 00:38, 15 September 2016

Theorem

Let $\mathbb{T}$ be a time scale and let $\epsilon > 0$. Then $$\dfrac{\mathbb{V}ar_{\mathbb{T}}(X) - \mathbb{E}_{\mathbb{T}}(2H(X))}{\epsilon^2} \geq P((X-\mathbb{E}_{\mathbb{T}}(X))^2 \geq \epsilon^2),$$ where the density function of $H(X)$ is $h_2(t,0)-\dfrac{t^2}{2}$.

Proof

References

$\Delta$-Inequalities

Bernoulli Bihari Cauchy-Schwarz Gronwall Hölder Jensen Lyapunov Markov Minkowski Opial Tschebycheff Wirtinger