Example 1: A coin is flipped. Random variable X takes the value 1 if the coin lands heads, and X takes the value 0 if the coin shows tails. Example 2: Three balls are drawn without replacement from a ...

Stochastic dominance (SD) theory is concerned with orderings of random variables by classes of utility functions characterized solely in terms of general properties. This paper discusses a type of ...

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, ...

This is a graduate-level course focused on techniques and models in modern discrete probability. Topics include: the first and second moment methods, martingales, concentration inequalities, branching ...

The main property of a discrete joint probability distribution can be stated as the sum of all non-zero probabilities is 1. The next line shows this as a formula. The marginal distribution of X can be ...

Stochastic dynamical systems arise in many scientific fields, such as asset prices in financial markets, neural activity in ...