# STAT400

STAT400 / MATH463: Statistics and Probability I, Fall 2018

Instructor: Xiaohui Chen (Office:104A Illini Hall).
Lecture (CL1): MWF 12:00pm — 12:50pm, 103 Mumford Hall.
Office Hours: M 1:00pm — 3:00pm, 104A Illini Hall.

Syllabus

TA and Grader:
— TA: Sayan Chakrabarty (sayanc3@illinois.edu).
— Grader: Zihao Yang (zihaoy3@illinois.edu).
Discuss Sessions:
— CD1: W 4:00pm — 4:50pm, 1027 Lincoln Hall.
— CD2: R 4:00pm — 4:50pm, 31 Psychology B.
— CD3: R 1:00pm — 1:50pm,1027 Lincoln Hall.
— CD4: R 8:00am — 8:50am, 1065 Lincoln Hall.
TA Office Hours: M – R, 5:00pm – 6:50pm.
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: Aug. 27, 2018, M.
Last Day of Class: Dec. 12, 2018, W.

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
Aug. 27 (M):                                    Introduction
Aug. 29 (W):                                 Probability rules
Aug. 31 (F):                              Conditional probability

Week 2                                           Contents
Sep. 3 (M):                              Labor Day (no class)
Sep. 5 (W):                                   Bayes Theorem
Sep. 7 (F):                                    Independence

Week 3                                           Contents
Sep. 10 (M):                                  Enumeration
Sep. 12 (W):                            Discrete random variables
Sep. 14 (F):                                    Expectation

Week 4                                           Contents
Sep. 17 (M):                               Bernoulli, Binomial
Sep. 19 (W):                        Geometric, negative binomial
Sep. 21 (F):                          Moment generating functions

Week 5                                           Contents
Sep. 24 (M):                               Poisson process
Sep. 26 (W):                              Poisson distribution
Sep. 28 (F):                        Continuous random variables

Week 6                                           Contents
Oct. 1 (M):                                  Uniform, exponential
Oct. 3 (W):                                 Midterm exam I (in class)
Oct. 5 (F):                                     Gamma, Chi-square

Week 7                                           Contents
Oct. 8 (M):                                   Gaussian/normal
Oct. 10 (W):                         Normal and related distributions
Oct. 12 (F):                                      Covariance

Week 8                                           Contents
Oct. 15 (M):                            Correlation coefficients
Oct. 17 (W):                    Several independent random variables
Oct. 19 (F):                       Chebyshev inequalities and applications

Week 9                                           Contents
Oct. 22 (M):                Central limit theorem (CLT) & normal approximation
Oct. 24 (W):                Central limit theorem (CLT) & normal approximation
Oct. 26 (F):                             Maximum likelihood estimator (MLE)

Week 10                                           Contents
Oct. 29 (M):                                         MLE
Oct. 31 (W):                        Method of moments estimator
Nov. 2 (F):                                Midterm exam II (in class)

Week 11                                           Contents
Nov. 5 (M):                                Evaluate estimators
Nov. 7 (W):                     Confidence intervals (CI) for means
Nov. 9 (F):                              Sample size calculations

Week 12                                           Contents
Nov. 12 (M):                                    CI for variances
Nov. 14 (W):                                    CI for proportions
Nov. 16 (F):                                    Hypothesis testing

Week 13                                           Contents

Thanksgiving week (no class)

Week 14                                           Contents
Nov. 26 (M):                                 Test for proportions
Nov. 28 (W):                                 Test for means
Nov. 30 (F):                                  Test for variances

Week 15                                           Contents
Dec. 3 (M):                             Test for equality of two means
Dec. 5 (W):
Dec. 7 (F):

Week 16                                           Contents
Dec. 10 (M):
Dec. 12 (W):

Final Exam:1:30-4:30 p.m., Friday, Dec. 14 @103 Mumford Hall (classroom).