Program Overview

Program Overview

The university program in question is a course on Probability and Statistical Inference, denoted as Math 40, offered during Winter 2023.

Instructors

The instructor for this course is Yoonsang Lee.

Syllabus

The syllabus for this course is outlined below:

Lecture Plan

The following plan is tentative and subject to changes. Note that the numbers in parentheses represent the corresponding sections of the textbook.

• Lecture 01: Basic probability
• Lecture 02: Binomial and Poisson distributions (1.2, 1.3, 1.4, 1.6, 1.7)
• Lecture 03: Poisson distributions (1.7), Distribution and density functions (2.1)

Chapter 2: Continuous Random Variables

• Lecture 04: Exponential Gamma, and Beta distributions (2.2, 2.3, 2.4, 2.6, 2.14)
• Lecture 05: Exponential Gamma, and Beta distributions (2.2, 2.3, 2.4, 2.6, 2.14)
• Lecture 06: Moment generating functions, Normal and lognormal distributions
• Lecture 07: Chebyshev’s inequality (2.8), Law of large numbers and central limit theorem (2.9, 2.10)
• Lecture 08: Transformations and the delta method (2.12, 2.13)

Chapter 3: Multivariate Random Variables

• Lecture 09: Joint CDF (3.1)
• Lecture 10: Independence (3.2)
• Lecture 11: Conditional density (3.3)
• Lecture 12: Correlation and linear regression (3.4)
• Lecture 13: Bivariate normal distribution (3.5)
• Lecture 14: Joint density upon transformations (3.6), Optimal portfolio allocations (3.8)
• Lecture 15: Multidimensional random vectors (3.10)
• Lecture 16: Review

Midterm Test

• Chapter 4: Four important distributions in statistics
  • Lecture 17 and 18: Chi-square distribution (4.2), t- and F-distributions (4.3, 4.4)

Chapter 6: Parameter Estimation

• Lecture 19: Statistics as inverse probability (6.1), Method of moments (6.2), Method of Quantiles (6.3)
• Lecture 20: Statistical properties of an estimator (6.4)
• Lecture 21 and 22: Linear estimation (6.5), Estimation of variance and correlation coefficient (6.6), Least squares (6.7)
• Lecture 23: Maximum likelihood (6.10)

Chapter 7: Hypothesis Testing and Confidence Intervals

• Lecture 24: Hypothesis testing (7.1, 7.2), Z, t, and chi-sq tests (7.3, 7.4)
• Lecture 25: Z, t, and chi-sq tests (7.3, 7.4), Variance and inverse CDF tests (7.5, 7.6)
• Lecture 26: Other hypothesis tests (7.7)
• Lecture 27: Confidence interval (7.8)

Final Exam

The final exam, which is comprehensive, is scheduled for March 10 (Friday) at 08:00 am.