ThmDex – An index of mathematical definitions, results, and conjectures.
F9599
Formulation 0
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number.
Let $\lambda > 0$ be a D5407: Positive real number.
Then \begin{equation} \mathbb{P}(X \geq \lambda) \leq \inf_{t \in [0, \infty)} \frac{1}{e^{t \lambda}} \mathbb{E}(e^{t X}) \end{equation}