Probability theory forms the mathematical backbone for quantifying uncertainty and random events, providing a rigorous language with which to describe both everyday phenomena and complex scientific ...

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical ...

Julie Young is an experienced financial writer and editor. She specializes in financial analysis in capital planning and investment management. Suzanne is a content marketer, writer, and fact-checker.

We give necessary and sufficient conditions for $P(\sum{_{n=1}^{\infty}}(A + S_{n})^{-1} < \infty) = 1$ in terms of E(∑n=1 ∞(A + Sn)-1), where Sn is the sum of n ...