Delta Markov inequality

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Theorem[edit]

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[edit]

References[edit]

$\Delta$-Inequalities

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