algo prob review1 annotated
DESCRIPTION
Algorithm ProbabilityTRANSCRIPT
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Probability Review
Part IDesign and Analysis
of Algorithms I
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Tim Roughgarden
Topics Covered• Sample spaces• Events• Random variables• Expectation• Linearity of ExpectationSee 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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1361121612
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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1𝑛
141234
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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6 .577.5
8
What is the expectation of the sum of two dice?
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𝑛4
𝑛3
𝑛2
3𝑛4
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)