probability review part i design and analysis of algorithms i
TRANSCRIPT
Probability Review
Part IDesign and Analysis
of Algorithms I
Tim Roughgarden
Topics Covered• Sample spaces• Events• Random variables• Expectation• Linearity of ExpectationSee also:• Lehman-Leighton notes (free PDF)• Wikibook on Discrete Probability
Tim Roughgarden
Concept #1 – Sample Spaces
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Concept #2 – Events
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?
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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Concept #2 – Events
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Concept #3 - Random Variables
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Concept #4 - Expectation
6 .577.5
8
What is the expectation of the sum of two dice?
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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Concept #4 - Expectation
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Concept #5 – Linearity of Expectation
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Linearity of Expectation (Proof)
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Example: Load Balancing
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Load Balancing Solution
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Load Balancing Solution (con’d)