Prerequisites: Math 4710 (Basic probability) or equivalent, and knowledge of linear algebra (e.g., Math 2210). Recommended: some knowledge of multivariable calculus.
Lecturer: Michael Nussbaum, <mn66>, 441 Malott, 5-3403, Office hours: T, F 2:30-3:30
Lecture: TR 11:40-12:55, 207 Malott Hall
Course Website: www.math.cornell.edu/~web4720 for initial summary; for the ongoing course http://blackboard.cornell.edu
TA: Wenyu Zhang, <wz258>, Office hours Tue 3:00 - 5:00 pm, Malott 218
Required Text:
DeGroot and Schervish, Probability and Statistics (Edition: 4) Pearson Education, 2010 (ISBN: 0-321-50046-5)
Description: Statistics have proved to be an important research tool in nearly all of the physical, biological, and social sciences. This course serves as an introduction to statistics for students who already have some background in calculus, linear algebra, and probability theory. The course will focus on the most important methods of inference usually taught in non-calculus introductory courses like Math 1710. The level of presentation however will be more rigorous and advanced, enabling not only an intuitive but also a mathematical understanding of these basic and commonly used methods. Topics will include inference for proportions (hypothesis tests and confidence intervals), inference for means (t-tests and t-intervals), inference in contingency tables (chi-square test) and basic linear regression.
Homework: (graded) Sets of exercises assigned weekly. While you may discuss these with others and get help from the instructor or the TA, the final work you submit must be your own. Late homework may be accepted (until solutions have been posted online) at a penalty of 10% per day. Electronic submissions not accepted.
Attendance policy: Use of laptops and other mobile electronic devices during lecture is not permitted. Violations will incur negative participation points for each instance. These will influence the final course score.
Exams:
Prelim 1: Thu 3/10 in class
Prelim 2: Thu 4/21 in class
Final: TBA
Grading: Your grade will be calculated as follows:
Homework 20%
Prelim 1 20%
Prelim 2 25%
Final exam 35%
The textbook also covers basic probability, which is a prerequisite here. We first describe the topics of the pertaining course (Math 4710) with chapter references based on: Ross, A First Course in Probability, 8th Edition, along with references in the present textbook.
Topic |
Ross |
deGroot, Schervish |
Methods of counting (combinatorics)
Axioms of probability
Conditional probability and independence |
Chapters 1-3 |
1.6-1.8
1.5
2.1-2.3 |
discrete (integer valued) random variable
-Bernoulli, binomial, Poisson distributions
-geometric, negative binomial distributions
continuous (real valued) random variables
-uniform, normal (Gaussian), exponential distributions
jointly distributed random variables |
Chapters 4-6 |
3.1
5.2, 5.4
5.5
3.2, 3.3
3.2, 5.6, 5.7
3.4-3.9 |
Expectations of sums of random variables
Covariance, variance of sums, and correlations
Conditional expectations
Moment generating functions |
Chapter 7 |
4.1, 4.2
4.3, 4.6
4.7
4.4 |
Weak law of large numbers, Central limit theorem |
Chapter 8 |
6.2, 6.3 |
The following represents a tentative outline of our course. Some textbook sections from above appear again below, indicating a recap and /or extension of the topic.
Topic |
deGroot, Schervish |
The mean and the median
Conditional expectation as prediction
The sample mean and the law of large numbers
The normal distribution
The central limit theorem |
4.5
4.7
6.1, 6.2
5.6
6.3 |
Statistical inference
Prior and posterior distributions
Beta and Gamma distributions
Conjugate prior distributions
Bayes estimators
Maximum likelihood estimators |
7.1
7.2
5.8, 5.7
7.3
7.4
7.5 |
The sampling distribution of a statistic
The chi square distribution
Joint distribution of sample mean and variance
The t distribution
Confidence intervals |
8.1
8.2
8.3
8.4
8.5 |
Problems of testing hypotheses
The t test
Comparing the means of two normal distributions |
9.1
9.5
9.6 |
Tests of Goodness-of-Fit
Contingency tables
Tests of homogeneity |
10.1
10.3
10.4 |
Linear statistical models: the method of least squares
The bivariate normal distributions
Regression
Statistical inference in simple linear regression
Analysis of variance |
11.1
5.10
11.2
11.3
11.6 |
In addition, Chap 12 (Simulation) may be treated, time permitting.