Difference between revisions of "Delta Markov inequality"
From timescalewiki
(Created page with "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 prob...") |
|||
| Line 1: | Line 1: | ||
Let $\mathbb{T}$ be a time scale with $a \in \mathbb{T}$. Then | 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]]. | + | where $X$ is a [[random variable]], $P$ denotes probability, and $\mathbb{E}_{\mathbb{T}}$ denotes [[expected value]]. |
Revision as of 22:03, 21 November 2014
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.
