Math 4720 Statistics, Spring 2016

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.