βMath
6. Conditional Expectation
date
Jun 21, 2023
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mat2017-6
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Public
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Statistics
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βMath
updatedAt
Jun 21, 2023 03:17 AM
6. Conditional ExpectationConditional ExpectationConditioning first stepRulesMore RulesExampleSticksMax(X,Y), Min(X,Y)GeneticChess tournamentsDiseaseEmailsStockBorn in March of next yearTask
6. Conditional Expectation
Conditional Expectation
Conditioning first step
- : first Heads in a sequence
Β
- Repeatedly
- expected # of tosses until the pattern HT first time
- expected # of tosses until the pattern HH first time
- (μμ 2λ E(W_HH)=2, λ€μ 2λ βHTβ λμ§)
- (1μ βTβ λμ§)
Rules
More Rules
Example
Sticks
Max(X,Y), Min(X,Y)
Genetic
- Identical twins:
- Fraternal twins:
Chess tournaments
Disease
Emails
- T: waiting times btw emails, X: first non-spam email arrives, N: # of emails until the first non-spam
Stock
- Low volatility:
- High volatility:
Born in March of next year
Task
