When G is a rooted graph where each edge may independently succeed with probability p, we consider the expected number of vertices in the operational component of G containing the root. This expected value EV (G;p) is a polynomial in p. We present several distinct equivalent formulations of EV (G;p), unifying prior treatments of this topic. We use results on network resilience (introduced by Co...

1. A random variable is a variable that takes specific values with specific probabilities. It can be thought of as a variable whose value depends on the outcome of an uncertain event. 2. We usually denote random variables by capital letters near the end of the alphabet; e.g., X,Y,Z. 3. Example: Let X be the outcome of the roll of a die. Then X is a random variable. Its possible values are 1, 2,...

Decision making is informed by appraisals of appetitive cues and their associated opportunities for rewards. Such appraisals can be modulated by cognitive regulation strategies in order to promote goal-directed choices. Little is known about how cognitive regulation strategies, especially reappraisal, alter risk taking during decision making. To characterise the effect of reappraisal on risk ta...

Anticipated reward magnitude and probability comprise dual components of expected value (EV), a cornerstone of economic and psychological theory. However, the neural mechanisms that compute EV have not been characterized. Using event-related functional magnetic resonance imaging, we examined neural activation as subjects anticipated monetary gains and losses that varied in magnitude and probabi...

In this paper, we explore a distributionally robust reinsurance problem that incorporates the concepts of Glue Value-at-Risk and expected value premium principle. The focuses on stop-loss contracts with known mean variance loss. optimization can be formulated as minimax problem, where inner involves maximizing over all distributions same variance. It is demonstrated represented either three-poi...