Difference between revisions of "Delta Markov inequality"

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Let $\mathbb{T}$ be a time scale with $a \in \mathbb{T}$. Then
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__NOTOC__
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==Theorem==
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Let $\mathbb{T}$ be a [[time scale]] with $a \in \mathbb{T}$. Then
 
$$P(X \geq a) \leq \dfrac{\mathbb{E}_{\mathbb{T}}(X)}{a},$$
 
$$P(X \geq a) \leq \dfrac{\mathbb{E}_{\mathbb{T}}(X)}{a},$$
where $X$ is a [[random variable]], $P$ denotes probability, and $\mathbb{E}$ denotes [[expected value]].
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where $X$ is a [[random variable]], $P$ denotes probability, and $\mathbb{E}_{\mathbb{T}}$ denotes [[expected value]].
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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 00:37, 15 September 2016

Theorem

Let $\mathbb{T}$ be a time scale with $a \in \mathbb{T}$. Then $$P(X \geq a) \leq \dfrac{\mathbb{E}_{\mathbb{T}}(X)}{a},$$ where $X$ is a random variable, $P$ denotes probability, and $\mathbb{E}_{\mathbb{T}}$ denotes expected value.

Proof

References

$\Delta$-Inequalities

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