1. Probability Review Part I Design and Analysis of Algorithms I

2. Tim Roughgarden Topics Covered Sample spaces Events Random variables Expectation Linearity of Expectation See also: Lehman-Leighton notes (free PDF) Wikibook on Discrete Probability

3. Tim Roughgarden Concept #1 – Sample Spaces

4. Tim Roughgarden Concept #2 – Events

5. Template vertLeftWhite2 Consider the event (i.e., the subset of outcomes for which) “the sum of the two dice is 7”. What is the probability of this event?

6. Template vertLeftWhite2 Consider the event (i.e., the subset of outcomes for which) “the chosen pivot gives a 25-75 split of better”. What is the probability of this event?

7. Tim Roughgarden Concept #2 – Events

8. Tim Roughgarden Concept #3 - Random Variables

9. Tim Roughgarden Concept #4 - Expectation

10. Template vertLeftWhite2 What is the expectation of the sum of two dice?

11. Template vertLeftWhite2 Which of the following is closest to the expectation of the size of the subarray passed to the first recursive call in QuickSort?

12. Tim Roughgarden Concept #4 - Expectation

13. Tim Roughgarden Concept #5 – Linearity of Expectation

14. Tim Roughgarden Linearity of Expectation (Proof)

15. Tim Roughgarden Example: Load Balancing

16. Tim Roughgarden Load Balancing Solution

17. Tim Roughgarden Load Balancing Solution (con’d)