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 ...

Random analytic functions are a fundamental object of study in modern complex analysis and probability theory. These functions, often defined through power series with random coefficients, exhibit ...

Sample space, Field and Probability Measure. Axiomatic definition of Probability. Bayes' theorem. Repeated trials. Continuous and discrete random variables and their probability distribution and ...

The Annals of Probability, Vol. 36, No. 1 (Jan., 2008), pp. 143-159 (17 pages) It is shown that functions defined on {0, 1,..., r - 1}ⁿ satisfying certain conditions of bounded differences that ...

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 ...

Applicable Analysis and Discrete Mathematics, Vol. 10, No. 2 (October 2016), pp. 408-446 (39 pages) An associative Boolean tree is a plane rooted tree whose internal nodes are labelled by AND or OR ...

Probability, statistics, reliability and decision with applications in engineering. Probability of events, discrete and continuous random variables, probability density functions and distributions, ...