Difference between revisions of "Delta Markov inequality"
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| − | Let $\mathbb{T}$ be a time scale with $a \in \mathbb{T}$. Then | + | __NOTOC__ |
| + | ==Theorem== | ||
| + | Let $\mathbb{T}$ be a [[time scale]] with $a \in \mathbb{T}$. Then | ||
$$P(X \geq a) \leq \dfrac{\mathbb{E}_{\mathbb{T}}(X)}{a},$$ | $$P(X \geq a) \leq \dfrac{\mathbb{E}_{\mathbb{T}}(X)}{a},$$ | ||
where $X$ is a [[random variable]], $P$ denotes probability, and $\mathbb{E}_{\mathbb{T}}$ denotes [[expected value]]. | where $X$ is a [[random variable]], $P$ denotes probability, and $\mathbb{E}_{\mathbb{T}}$ denotes [[expected value]]. | ||
| + | |||
| + | ==Proof== | ||
| + | |||
| + | ==References== | ||
| + | |||
| + | {{:Delta inequalities footer}} | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[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 |
