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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

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CS 312: Algorithm Analysis

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  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

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