Instructors: Yoonsang Lee

Course on canvas.dartmouth.edu.

## Syllabus

### Lecture Plan

The following plan is tentative and subject to changes.

Note: the numbers in the parenthesis represents 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) Links to an external site.

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 (comprehensive) - March 10 (Fri) 08:00 am