Difference between revisions of "Delta Markov inequality"

From timescalewiki
Jump to: navigation, search
 
(3 intermediate revisions by the same user not shown)
Line 1: Line 1:
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