• MATH 697
  • Syllabus
    • General Information
    • Course Description
    • Grade Distribution
    • Target Syllabus
      • Overview and Descriptive Statistics (Weeks 1-4)
      • Probability (Weeks 1-4)
      • Discrete Random Variables and Probability Distributions (Weeks 1-4)
      • Continuous Random Variables and Probability Distributions (Weeks 5-8)
      • Joint Probability Distributions (Weeks 5-8)
      • Sampling Distributions and Limits (Weeks 5-8)
      • Statistical Inference (Weeks 9-12)
      • Likelihood Inference (Weeks 9-12)
      • Regression and Correlation (Weeks 9-12)
  • Prerequisites
    • Install R and RStudio
    • R Packages
    • Introduction to R
    • Background Reading
  • Slides
  • Assignments
  • Quiz
  • R Code
    • 0.1 Central Limit Theorem in Action
    • 0.2 IMPC Dataset
  • Distribution Tables
    • 0.3 Standard Normal
    • 0.4 t-Distribution
  • I Part I
  • 1 Overview and Descriptive Statistics
    • 1.1 Populations and Samples
      • 1.1.1 Variable
      • 1.1.2 Branches of Statistics
    • 1.2 Pictorial and Tabular Methods in Descriptive Statistics
    • 1.3 Measures of Location
    • 1.4 Measures of Variability
  • 2 Probability
    • Introduction
      • Probability: A Measure of Uncertainty
    • 2.1 Sample Spaces and Events
      • 2.1.1 Sample Spaces
      • 2.1.2 Events
    • 2.2 Axioms, Interpretations, and Properties of Probability
    • 2.3 Counting Techniques
      • 2.3.1 Permutations
      • 2.3.2 Combinations
    • 2.4 Conditional Probability
      • 2.4.1 Law of Total Probability
      • 2.4.2 Bayes’ Rule
    • 2.5 Independence
  • 3 Discrete Random Variables and Probability Distributions
    • Introduction
    • 3.1 Random Variables
    • 3.2 Probability Distributions for Discrete Random Variables
    • 3.3 Expected Values of Discrete Random Variables
    • 3.4 Moments and Moment Generating Functions
    • 3.5 The Binomial Probability Distribution
    • 3.6 The Poisson Probability Distribution
  • 4 Continuous Variables and Probability Distributions
    • Introduction
  • R Tutorial
  • A Vectorization, *apply and for loops
    • A.1 Vectorization
    • A.2 Family of *apply functions
      • A.2.1 Loops vs. Apply
      • A.2.2 Descriptive Statistics using *apply
      • A.2.3 Creating new columns using sapply
      • A.2.4 Applying functions to subsets using tapply
      • A.2.5 Nested for loops using mapply
    • A.3 Creating dynamic documents with mapply
  • B Appendix B
  • References
  • Published with bookdown

MATH 697

Slides

  1. Discrete Random Variables and Probability Distributions (part I)
  2. Discrete Random Variables and Probability Distributions (part II)
  3. Continuous Random Variables and Probability Distributions
  4. Normal Distribution and Expectations of Continuos Random Variables
  5. Transformations of a Random Variable and Discrete Joint Distributions
  6. Joint, Marginal, Conditional Continuous Distributions
  7. Multidimensional Change of Variables, Conditional Expectation, Variance, Hierarchical Distributions
  8. Sampling Distributions and Limits, Convergence in Probability
  9. Convergence in Distribution and Central Limit Theorem
  10. Maximum Likelihood Estimation
  11. A Primer on Linear Regression