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References for Random Variables

Curated resources to deepen your understanding of random variables, probability distributions, expected value, and the binomial and geometric distributions.

Wikipedia Articles

  1. Random Variable - Wikipedia - Comprehensive introduction to random variables, including discrete and continuous types, with mathematical foundations and practical examples used in statistics and probability theory.

  2. Expected Value - Wikipedia - Explains the concept of expected value as the long-run average outcome of a random variable, with formulas, properties, and applications in decision-making and gambling.

  3. Binomial Distribution - Wikipedia - Detailed coverage of the binomial distribution including the BINS conditions, probability formula, mean and variance formulas, and real-world applications in quality control and polling.

Textbooks

  1. The Practice of Statistics by Daren S. Starnes and Josh Tabor - W.H. Freeman (2018) - The standard AP Statistics textbook with clear explanations of random variables, expected value calculations, and extensive practice problems aligned with the AP curriculum.

  2. Statistics: Learning from Data by Roxy Peck and Tom Short - Cengage Learning (2018) - Offers accessible explanations of probability distributions and random variable concepts with numerous worked examples suitable for high school students.

Online Resources

  1. AP Statistics Course Description - College Board - The official course framework outlining learning objectives for random variables, probability distributions, and the binomial and geometric settings that appear on the AP exam.

  2. Khan Academy: Random Variables - Khan Academy - Free video tutorials covering discrete random variables, expected value, variance, and standard deviation with interactive practice exercises and immediate feedback.

  3. Stat Trek: Binomial Distribution Tutorial - Stat Trek - Step-by-step guide to understanding binomial probability with an online calculator for computing binomial probabilities, means, and standard deviations.

  4. Against All Odds: Inside Statistics - Annenberg Learner - Video series produced for PBS featuring real-world applications of probability distributions, including episodes on binomial and geometric models with compelling visual demonstrations.

  5. AP Statistics Review: Random Variables - Albert.io - Practice questions and explanations specifically designed for AP Statistics exam preparation, covering expected value, combining random variables, and distribution properties.