1 / 22

CS 312: Algorithm Analysis

This work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License . CS 312: Algorithm Analysis. Lecture #11: Review of Basic Probability Theory. Slides by: Eric Ringger. Announcements. Project #2 Due: today Code Reviews are good Project #3

hovan
Télécharger la présentation

CS 312: Algorithm Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. This work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License. CS 312: Algorithm Analysis Lecture #11: Review of Basic Probability Theory Slides by: Eric Ringger

  2. Announcements • Project #2 • Due: today • Code Reviews are good • Project #3 • Help session: Tuesday at 5pm • 1066 TMCB

  3. Objectives • Learn important ideas from probability theory • Prepare for the proof of the average case analysis of Quicksort

  4. Average Case Analysis • We know: • Quicksort takes in the worst case • and in the best case. • How would you approach an average case analysis of Quicksort?

  5. Average Case Analysis • How would you approach an average case analysis?

  6. Basic Probability Theory We need the following ideas: • Samples / Outcomes • Events • Probability Measures • Random Variables • Values of Random Variables • Expected value of random variable

  7. Samples

  8. Samples

  9. Events

  10. Sigma Field

  11. Probability Measure

  12. Probability Space

  13. Example: One Fair Die

  14. Probability in 3-D

  15. Random Variables

  16. Random Variables

  17. Values of Random Variables • We speak of values of x (in the range) as “events”, just as we did for subsets of the domain.

  18. Expected Value of RV

  19. Expected Value of RV

  20. Example

  21. Questions? • Samples / Outcomes • Events • Probability Measures • Random Variables • Values of Random Variables • Expected value of random variable

  22. Assignment • HW #8 – updated on schedule • Send me email with your chosen theorem

More Related