Math 526 - Applied Mathematical Statistics I

Fall 2018

TR 2:30--3:45 SNOW 120

Terry Soo, Snow 507

Office hours: Tuesday 4:15 - 5:15, Wednesday 2:30 - 3:30

Course description.

This is a calculus-based introduction to probability and statistics. We will introduce basic notions in probablity theory, culminating in a statement of the central limit theorem. Then we will apply our knowledge of probability to hypothesis testing. We will also introduce and use the free statistical software, R, which is widely used in industry and academia. By the end of this course you will have the tools to address the following questions.

Why is it so hard to get a perfect bracket? What numbers should I choose if I play the lottery? Is it so surprising that you have so many friends on Facebook with the same birthday? Why do all garbage trucks smell the same? How do we determine if a coin is fair or not? How can we verify a claim that someone can tell the difference between Coke and Pepsi?

Prerequisites.

Multivariable caluculus -- Math 127 or Math 147 recommmended. You should be able to do these problems Problems

Outline

Descriptive statistics: means, standard deviation, histograms, fitting a line

Probability theory: axioms of probability, sample spaces, set operations

Counting techniques

Stochastic Independence

Conditional probability: Bayes' theorem

Random variables (discrete and continuous): probability distribritions, expecation, law of large numbers

Poisson processes

The normal distribution and the central limit theorem

Random sampling

Point esimtators

Confidence intervals

Hypothesis testing

Grading

Subject to revision

Best of:

Scheme 1:

Quizzes 20%

Midterm I 10% (September 20)

M1

Midterm II 20% (October 30)

M2

R assignments 10%

Final Exam 40%

KU final exam schedule

Scheme 2:

Final exam 90%

R assignements 10%

There are no possibilities for make-up quizzes or midterms; if you have a legitimate excuse for missing an exam (for example, medical reasons), then the absense will be excused without penalty; in the case of quizzes, your other quizzes will simply be worth more, and in the case of a midterm, your final exam will be worth more.

No textbook is required. Lecture notes will be provided. Extensive course materials are also available from when I last taught the course: Math 526 2014

Download R

Suitable secondary references

Probability and statitics for engineers and scientists; Walpole, Myers, Myers, Ye; used previously and in other sections.

Probability and statistics for engineering and the sciences; Devore

An introduction to R; Venables, Smith, and the R Core team

Probability and random processes ; Grimmett and Stirazker; more advanced

Introduction to mathematical statistics ; Hogg, Mckean, Craig; more advanced

Casella and Berger; Statistical inference; more advanced

Quizzes:

Quizzes can cover material from grade 1 up to and including the previous day.

Quiz 1, Tuesday September 11

Quiz 2, Tuesday September 18

Quiz 3, Tuesday October 9

Quiz 4, Thursday October 18

Quiz 5, Thursday October 25

Quiz 6, Tuesday November 20: (will only cover up to and including Section 14 of the notes)

Homework:

Math 526 Homework: will be updated and edited throughtout the course

R homework is to be printed out and handed in class--no email submissions.

R Homework: Due September 4

R Homework: Due September 18

R Homework: Due October 25

R Homework: Due November 1

R Homework: Due November 20

Notes:

Math 526 Notes: will be updated and edited throughtout the course

Introduction to R

In class worksheet