Probability Review Part I Design and Analysis of Algorithms I.

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Presentation transcript:

Probability Review Part I Design and Analysis of Algorithms I

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

Tim Roughgarden Concept #1 – Sample Spaces

Tim Roughgarden Concept #2 – Events

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?

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

Tim Roughgarden Concept #2 – Events

Tim Roughgarden Concept #3 - Random Variables

Tim Roughgarden Concept #4 - Expectation

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

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?

Tim Roughgarden Concept #4 - Expectation

Tim Roughgarden Concept #5 – Linearity of Expectation

Tim Roughgarden Linearity of Expectation (Proof)

Tim Roughgarden Example: Load Balancing

Tim Roughgarden Load Balancing Solution

Tim Roughgarden Load Balancing Solution (con’d)