Part 5: Probability & Random Variables

Covers: Topics 4.1 - 4.12 of the Course & Exam Description (CED)

Stats Content (CED Topics 4.1-4.3)

  • Definition & Properties of Probability

  • Probability Models

  • Law of Large Numbers

Relevant Context

  • Baseball

  • The “Curse” of the Home Run Derby


Stats Content (CED Topics 4.4 & 4.6)

  • Unions & Intersections

  • The Addition Rule

  • Two-Way Tables, Venn Diagrams

Relevant Context

  • Do people lie in their online dating profiles?


Stats Content (CED Topics 4.5-4.6)

  • Conditional Probability

  • Independence & Multiplication Rule

  • Tree Diagrams

Relevant Context

  • Do people lie in their online dating profiles?


Stats Content (CED Topics 4.5-4.6)

  • Successive Independent Events

  • “At Least One” Scenarios

  • Sampling Without Replacement

Relevant Context

  • Kobe’s 81-Point Game

  • “Hot Hand” Theory


Stats Content (CED Topics 4.7-4.8)

  • Discrete Random Variables

  • Probability Distributions

  • Expected Value

Relevant Context

  • Gambling

  • How Casinos Make $$$


Stats Content (CED Topics 4.8-4.9)

  • Variance & Standard Deviation

  • Transforming Random Variables

  • Combining Random Variables

Relevant Context

  • Gambling

  • How Casinos Make $$$


Stats Content (CED Topics 4.10-4.12)

  • Geometric Distribution

  • Binomial Distribution

  • PDF vs. CDF

Relevant Context

  • Basketball

  • “Granny” Free Throws

 
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Part 4: Sampling & Experiments

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Part 6: Sampling Distributions