STAT400

STAT400 / MATH463: Statistics and Probability I, Spring 2017

Instructor: Xiaohui Chen (Office:104A Illini Hall).
Lecture (BL1): TR 12:30pm — 1:50pm, 180 Bevier Hall.
Office Hours:TR 2:00pm — 3:00pm, 104A Illini Hall.

Syllabus

Course TAs:
— Teng Wu (tengwu2@illinois.edu).
— Yujia Deng (yujiad2@illinois.edu).
Discuss Sessions:
— BD1: W 11:00am — 11:50am, 331 Armory (Wu).
— BD2: W 4:00pm — 4:50pm, 138 Henry Administration Bldg (Deng).
— BD3: W 2:00pm — 2:50pm,1027 Lincoln Hall (Deng).
— BD4: W 12:00pm — 12:50pm, 1027 Lincoln Hall (Wu).
Help Room/Tutor Hours: M – R, 5:00pm – 6:50pm, Room 2, Illini Hall.
Course Website: Course syllabus, lecture notes and slides will be posted on the Compass 2g. Homework assignments will be posted, electronically submitted and graded through the LON-CAPA system.
Prerequisite: MATH 241 Calculus III.

Announcements:
— Welcome!
— First Day of Class: Jan. 17, 2017, T.
Last Day of Class: May 2, 2017, T.


Text: Robert V. Hogg, Elliot A. Tanis, Dale L. Zimmerman. Probability and Statistical Inference. Ninth Edition. Pearson.

Topics: This is an introductory course to mathematical statistics that develops probability as needed. Topics to be covered are:

1. Probability and random variables (Ch.1)
2. Discrete and continuous distributions (Ch.2-4)
3. The central limit theorem and normal approximation (Ch.5)
4. Point estimation and confidence intervals (Ch.6-7)
5. Hypothesis testing (Ch.8)

Please see the following tentative schedule for details.

Course Plan/Progress (Tentative)

Week 1                                          Contents
Jan. 17 (T):                                    Introduction
Jan. 19 (R):                 Probability rules, Conditional probability

Week 2                                          Contents
Jan. 24 (T):                                Bayes Theorem
Jan. 26 (R):                                  Independence

Week 3                                          Contents
Jan. 31 (T):                                    Enumeration
Feb. 2 (R):                Discrete random variables, expectation

Week 4                                          Contents
Feb. 7 (T):           Bernoulli, Binomial, Geometric, neg binomial
Feb. 9 (R):                        Moment generating functions

Week 5                                          Contents
Feb. 14 (T):                    Poisson process and distribution
Feb. 16 (R):                     Continuous random variables

Week 6                                          Contents
Feb. 21 (T):                                    Midterm I
Feb. 23 (R):                              Uniform, exponential

Week 7                                          Contents
Feb. 28 (T):                              Gamma, Chi-square
Mar. 2 (R):                                 Normal/Gaussian

Week 8                                          Contents
Mar. 7 (T):                        Normal and related distributions
Mar. 9 (R):                      Two random variables, covariance

Week 9                                          Contents
Mar. 14 (T):                 Covariance, correlation coefficients
Mar. 16 (R):                                    Midterm II

Week 10                                         Contents

                                          Spring vacation, no class

Week 11                                         Contents
Mar. 28 (T):          Several independent random variables, Chebyshev
Mar. 30 (R):         Central limit theorem (CLT) & normal approximation

Week 12                                         Contents
Apr. 4 (T):                  Maximum likelihood estimator (MLE)
Apr. 6 (R):               Method of moments estimator, unbiasedness

Week 13                                         Contents
Apr. 11 (T):            Confidence intervals (CI) for means, sample size
Apr. 13 (R):                       CI for variances and proportions

Week 14                                         Contents
Apr. 18 (T):                                     Midterm III
Apr. 20 (R):                Hypothesis testing, test for proportions

Week 15                                         Contents
Apr. 25 (T):                          Test for means & variances
Apr. 27 (R):                         Test for equality of two means

Week 16                                         Contents
May. 2 (T):                                         Review

Final Exam: May 8, 2017 (Monday), 1:30pm — 4:30pm,180 Bevier Hall.