Discrete Probability and Average-Case Complexity

  • Tom Jenkyns
  • Ben Stephenson
Chapter
Part of the Undergraduate Topics in Computer Science book series (UTICS)

Abstract

Discrete probability is introduced as a method to estimate average cases, not to predict individual outcomes from a process subject to chance or unpredictability, like flipping a coin or rolling a die.

Basic definitions are given for the fundamental concepts: an experiment, a sample space, a probability function, events, independent events, conditional probability, random variables, and the expected value of a random variable. Expected value generalizes average value and is used for calculating the average-case complexity of algorithms.

Standard distributions, which are good models of many real-world processes including computer applications, are treated in some detail. These include the uniform distribution, the binomial distribution, and the geometric distribution.

This chapter ends with a proof that the average-case complexity of QuickSort is O(nlgn).

Keywords

Conditional Probability Probabilistic Model Probability Function Sample Space Geometric Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Tom Jenkyns
    • 1
  • Ben Stephenson
    • 2
  1. 1.Department of MathematicsBrock UniversitySt. CatharinesCanada
  2. 2.Department of Computer ScienceUniversity of CalgaryCalgaryCanada

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