ORF 245: Statistics

Lectures Based on

Mathematical Statistics and Data Analysis (by John A. Rice)

- Chapter 1: Probability
- Chapter 2: Random Variables
- Chapter 3: Joint Distributions
- Chapter 4: Expected Values
- Chapter 5: Limit Theorems
- Chapter 6: Distributions Derived from the Normal Distribution
- Chapter 7: Confidence Intervals
- Chapter 8: Parameter Estimation and Distribution Fitting
- Chapter 9: Hypothesis Testing and Goodness of Fit
- Chapter 10: Summarizing Data
- Chapter 14: Linear Least Squares

- Sun, Nov 16, 2014: Sec. 9.1, 9.2, 9.3
- Mon, Nov 10, 2014: Sec. 8.1-8.5
- Sat, Nov 1, 2014: Sec. 7.1, 7.2, 7.3 (skip 7.3.1 Lemma B, Thm. B, and Cor. B)
- Mon, Sept 29, 2014: Sec. 3.4-3.6
- Mon, Sept 22, 2014: pp 54-64, Sec. 3.1-3.3
- Fri, Sept 19, 2014: pp 47-54
- Wed, Sept 17, 2014: pp 35-47
- Mon, Sept 15, 2014: pp 1-40

- Basics of probability including the definition of a sample space and probabilities of events defined on the sample space.
- Indepedent events.
- Random variables cumulative distribution function, and density function.
- The most common/important discrete and continuous random variables.
- Independent random variables.
- Joint distribution, marginal and conditional distributions.
- Bayesian Inference.
- Expectation, mean, and variance.
- Collections of independent identically distributed random variables.
- Sample mean and sample variance.
- Central Limit Theorem.
- Confidence intervals for the mean.
- Method of Moments (MoM) and Maximum Likelihood Estimators (MLE).
- Confidence intervals based on t-distribution.
- Hypothesis Testing.
- Linear Regression.

Throughout the course, we will use the computer language Matlab to perform computations on real-world data to illustrate the methods and ideas covered in the course. The data sets will span from historical stock market prices to temperature data needed to study climate change.

- Homeworks due every Friday, 5:00pm. 10% off for each day (or part of a day) thereafter.
- At the end of the semester, the lowest homework grade will be dropped
- Two midterms (Friday October 17 and Friday December 5).
- Final grade based on:
- Homework:

45% - Midterm 1:

15% - Midterm 2:

15% - Final:

20% - Participation:

5% - Precepts: 3:30-4:20pm and 7:30-8:20pm on Mondays and Tuesdays.
- Office Hours:
- Mon -- Ziwei Zhu

2:00pm to 3:30pm, Sherrerd 218. - Tue -- Tianqi Zhao

11:00am to 12:30pm, Sherrerd 324. - Wed -- Byron Vickers

2:30pm to 4:00pm, Sherrerd 219. - Thu -- Raymond Perkins

10:00am to 11:30 am, Sherrerd 002. - Thu -- Weichen Wang

3:00pm to 4:30pm, Sherrerd 220. - Fri -- Prof. Vanderbei

1:30pm to 3:00pm, Sherrerd 209. - Old Midterms: click here