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Quantitative MethodsModule 4 of 11

Probability Trees and Conditional Expectations

6

Concepts

4

Formulas

1

Decisions

4

Quiz Questions

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Key Concepts

6 concepts covered in this module.

Expected Value

E(X) = Σ P(xi) × xi. The probability-weighted average of all possible outcomes.

Conditional Probability

P(A|B) = P(AB) / P(B). The probability of A given that B has occurred.

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Formulas

4 essential formulas for this module.

Expected Value

E(X) = Σ P(xi) × xi

Where: P(xi) = probability of outcome i

Bayes' Formula

P(B|A) = [P(A|B) × P(B)] / P(A)

Where: P(B) = prior, P(B|A) = posterior

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Decision Frameworks

1 decision frameworks to guide your analysis.

When to use Bayes' Formula?

  • Updating probability estimates with new evidence
  • Medical/diagnostic testing problems
  • Revising economic forecasts with new data

Mind Map

Visual overview of how concepts connect in this module.

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Expected Value

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Answer
E(X) = Σ P(xi) × xi. The probability-weighted average of all possible outcomes.
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