Course Syllabus

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Instructor: Yoonsang Lee (yoonsang.lee@dartmouth.edu) @ 206 Kemeny

Prerequisites: Math 11/13 and Math 20

Class hours: MWF 8:50 - 9:55 am @ 007 Kemeny

X-hour: Th 9:05 - 9:55 am

Office hours: MWF 10-10:30 am, W 1:30 - 2:30 pm, Th 9-10:30 am

Textbook: E. Demidenko, Advanced Statistics with Applications in R, Wiley Series in Probability and Statistics

Other references: An Introduction to Mathematical Statistics and Its Applications by Larsen and Marx

Assessment & Grading
The homework and tests include problems to measure quantitative (calculation) and qualitative (proof) understanding of the materials. The grading will be based on the following contributions:

  • Homework assignments 40% (four sets before the midterm, and the other four sets after the midterm)
  • Midterm 20% 
  • Final 35%
  • Survey 5%
  • Missing more than two lectures will degrade your letter grade, ex) A- -> B-, C+ -> D+.

Ex) if you have an A- based on the four categories (homework, midterm, final, survey), but
i) miss more than two lectures, A- => B-
ii) miss more than four lectures, A- => C-
iii) miss more than six lectures, A- => D-.

Lecture Plan

The following plan is tentative and subject to changes.

Note: the numbers in the parentheses represent the corresponding sections of the textbook.

  • Basic Probability
  • Binomial and Poisson distributions (1.2, 1.3, 1.4, 1.6, 1.7)
  • Poisson distributions (1.7), Distribution and density functions (2.1)

Chapter 2 Continuous random variables

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

Chapter 3 Multivariate random variables

  • Joint CDF (3.1) 
  • Independence (3.2) 
  • Conditional density (3.3)
  • Correlation and linear regression (3.4) 
  • Bivariate normal distribution (3.5) 
  • Joint density upon transformations (3.6), Optimal portfolio allocations (3.8) 
  • Multidimensional random vectors (3.10)
  • Review

Midterm (in class)

Chapter 4 Four important distributions in statistics

  • Chi-square distribution (4.2), t- and F-distributions (4.3, 4.4)

Chapter 6 Parameter estimation

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

Chapter 7 Hypothesis testing and confidence intervals

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

Final exam (comprehensive): March 15 (Sunday) 11:30 am - 2:30 pm

Course Summary:

Course Summary
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