Math 159 Notes: Discrete Probabilistic Methods

Some Identities involving the Partial Sum of q-Binomial Coefficients

We give some identities involving sums of powers of the partial sum of q-binomial coefficients, which are q-analogues of Hirschhorn’s identities [Discrete Math. 159 (1996), 273–278] and Zhang’s identity [Discrete Math. 196 (1999), 291–298].

DISCRETE OPTIMIZATION Notes prepared for : MATH 2602 Linear and Discrete Mathematics

Notes by Dave Edwards Discrete Probability

Monte Carlo integration is a powerful method for computing the value of complex integrals using probabilistic techniques. This document explains the math involved in Monte Carlo integration. First I give an overview of discrete random variables. Then I show how concepts from discrete random variables can be combined with calculus to reason about continuous random variables. Finally, with a know...

Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra

We consider stochastic programming problems with probabilistic constraints in volving random variables with discrete distributions They can be reformulated as large scale mixed integer programming problems with knapsack constraints Using speci c properties of stochastic programming problems and bounds on the prob ability of the union of events we develop new inequalities for these mixed integer...

Improvements to exact Boltzmann sampling using probabilistic divide-and-conquer and the recursive method