Difference between revisions of "Delta Tschebycheff inequality"
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$$\dfrac{\mathbb{V}ar_{\mathbb{T}}(X) - \mathbb{E}_{\mathbb{T}}(2H(X))}{\epsilon^2} \geq P((X-\mathbb{E}_{\mathbb{T}}(X))^2 \geq \epsilon^2),$$ | $$\dfrac{\mathbb{V}ar_{\mathbb{T}}(X) - \mathbb{E}_{\mathbb{T}}(2H(X))}{\epsilon^2} \geq P((X-\mathbb{E}_{\mathbb{T}}(X))^2 \geq \epsilon^2),$$ | ||
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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Revision as of 23:38, 28 March 2015
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 $h_2(t,0)-\dfrac{t^2}{2}$.
$\Delta$-Inequalities
| Bernoulli | Bihari | Cauchy-Schwarz | Gronwall | Hölder | Jensen | Lyapunov | Markov | Minkowski | Opial | Tschebycheff | Wirtinger |
