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Part I

Probability Review. Part I. Design and Analysis of Algorithms I. Topics Covered. Sample spaces Events Random variables Expectation Linearity of Expectation See also: Lehman-Leighton notes (free PDF) Wikibook on Discrete Probability. Concept #1 – Sample Spaces. Concept #2 – Events.

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Part I

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

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

  3. Concept #1 – Sample Spaces

  4. Concept #2 – Events

  5. 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. 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. Concept #2 – Events

  8. Concept #3 - Random Variables

  9. Concept #4 - Expectation

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

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

  12. Concept #4 - Expectation

  13. Concept #5 – Linearity of Expectation

  14. Linearity of Expectation (Proof)

  15. Example: Load Balancing

  16. Load Balancing Solution

  17. Load Balancing Solution (con’d)

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