Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, moment generating functions, law of large numbers, ...

Let (Ω, F, P) be a probability space, and let X be a random variable defined on (Ω, F, P). If A is a sub σ-field of F, then E(X ∣ A) is the a.s. unique A measurable function such that, for all A ε A, ...

In this paper, convergence of series and almost sure convergence are established for weighted random variables under a sub-linear expectation space. Our results are very extensive versions which ...

Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time. Queuing theory, terminology, and single queue systems are studied with ...

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 ...

What Is A Probability Density Function? A probability density function, also known as a bell curve, is a fundamental statistics concept, that describes the likelihood of a continuous random variable ...