Probability and Statistics III: A Gentle Introduction to Statistics

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“FCPS” refers to the free text, A First Course in Probability and Statistics: free access is provided via a PDF file or as a book

Module 1: Distributions
• Lesson 1: Bernoulli and Binomial Distributions (FCPS §4.1.1)
• Lesson 2: Hypergeometric Distribution (FCPS §4.1.2)
• Lesson 3: Geometric and Negative Binomial Distributions (FCPS §4.1.3)
• Lesson 4: Poisson Distribution (FCPS §4.1.4)
• Lesson 5: Uniform, Exponential, and Friends (FCPS §4.2.1–4.2.2)
• Lesson 6: Other Continuous Distributions (FCPS §4.2.3)
• Lesson 7: Normal Distribution: Basics (FCPS §4.3.1)
• Lesson 8: Standard Normal Distribution (FCPS §4.3.2)
• Lesson 9: Sample Mean of Normals (FCPS §4.3.3)
• Lesson 10: The Central Limit Theorem + OPTIONAL Proof (FCPS §4.3.4)
• Lesson 11: Central Limit Theorem Examples (FCPS §4.3.5)
• Lesson 12 [OPTIONAL]: Extensions – Multivariate Normal Distribution (FCPS §4.4.1)
• Lesson 13 [OPTIONAL]: Extensions – Lognormal Distribution (FCPS §4.4.2)
• Lesson 14: Computer Stuff, including OPTIONAL Box-Muller Proof (FCPS §4.5)

Module 2: Getting Started with Statistics
• Lesson 1: Introduction to Descriptive Statistics (FCPS §5.1.1)
• Lesson 2: Summarizing Data (FCPS §5.1.2)
• Lesson 3: Candidate Distributions (FCPS §5.1.3)
• Lesson 4: Introduction to Estimation (FCPS §5.2.1)
• Lesson 5: Unbiased Estimation (FCPS §5.2.2)
• Lesson 6: Mean Squared Error (FCPS §5.2.3)
• Lesson 7: Maximum Likelihood Estimation (FCPS §5.2.4)
• Lesson 8: Trickier MLE Examples (FCPS §5.2.4)
• Lesson 9: Invariance Property of MLEs (FCPS §5.2.4)
• Lesson 10: Method of Moments Estimation (FCPS §5.2.5)
• Lesson 11: Sampling Distributions (FCPS §5.3)

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