STA 9715 - Notes

Supplemental course notes will be posted here.

Week 1: Foundations of Probability

• Quanta Magazine: “Perplexing the Web, One Probability Puzzle at a Time”
• WIRED Magazine: “Statistician Answers Stats Questions From Twitter | Tech Support”
  • More Jeff Rosenthal
• Harvard STAT 110 Playlist
  • This is the course on which our textbook (BH) is based

Week 2: Conditionality and Marginality

• The YouTube channel 3blue1brown makes excellent ‘explainers’ about a variety of mathematical topics. Check out his videos on Bayes’ rule:
  • The Geometry of Changing Beliefs
    • See also A Quick Proof of Bayes Theorem
  • The Medical Test Paradox
• Conditioning: The Soul of Statistics
• Notes on Expectations

Week 3: Discrete Probability

• Notes on Discrete Distributions

Week 4: From Discrete to Continuous Random Variables

• Notes on Continuous Random Variables

Week 5: Heavy Tails

• Notes on Tails of Distributions and Implications for Statistical Inference

Week 6: Random Vectors

• Notes on Vectors
• Quanta Article on Probability Puzzles

Week 7: Covariance and Correlation

• Notes on Covariance

Week 8: The Multivariate Normal Distribution and its Progeny

• 3Brown1Blue - “Why \(pi\) is in the Normal Distribution”
• 3Brown1Blue - “A Pretty Reason why Gaussian + Gaussian = Gaussian”
• Multivariate Normal Distribution Notes

Week 9: Probability, Polling, and Prediction

• How the Washington Post Estimates Outstanding Votes for the 2020 Presidential Election

Week 10: Perils and Paradoxes in Expectations

Week 11: Probability Inequalities and Limit Theorems

Week 12: Distributional Limits and the Central Limit Theorem

Week 13: Concentration of Measure: Generalized Limit Theory

Week 14: Computing with Randomness

Exam Materials

• Test 1:
  • Formula Sheet
  • Exam Packet
  • Solutions
• Test 2:
  • Formula Sheet
  • Exam Packet
  • Solutions