# Difference between revisions of "Delta Tschebycheff inequality"

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==Theorem== | ==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 |

## 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 |