Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

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 ...

A random variable that can take only a certain specified set of individual possible values-for example, the positive integers 1, 2, 3, . . . For example, stock prices are discrete random variables, ...

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, ...

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

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

Description: A first course in probability intended to serve as a background for statistics and other applications. Sample spaces and axioms of probability, discrete and continuous random variables, ...