ORF 245: Statistics

Lectures Based on

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

Lecture Slides:

• 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

Reading Assignment:

• 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)
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• 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

Syllabus:

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

Course Info:

• 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 and Final Exams: click here