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Probability Review Part I Design and Analysis of Algorithms I
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Tim Roughgarden Topics Covered Sample spaces Events Random variables Expectation Linearity of Expectation See also: Lehman-Leighton notes (free PDF) Wikibook on Discrete Probability
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Tim Roughgarden Concept #1 – Sample Spaces
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Tim Roughgarden Concept #2 – Events
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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?
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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?
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Tim Roughgarden Concept #2 – Events
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Tim Roughgarden Concept #3 - Random Variables
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Tim Roughgarden Concept #4 - Expectation
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Template vertLeftWhite2 What is the expectation of the sum of two dice?
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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?
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Tim Roughgarden Concept #4 - Expectation
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Tim Roughgarden Concept #5 – Linearity of Expectation
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Tim Roughgarden Linearity of Expectation (Proof)
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Tim Roughgarden Example: Load Balancing
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Tim Roughgarden Load Balancing Solution
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Tim Roughgarden Load Balancing Solution (con’d)
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