stat310

Syllabus

Stat310 is a calculus based introduction to mathematical statistics. The course will cover basic probability, random variables (continuous and discrete), multivariate distributions, the central limit theorem and statistical inference, including parameter estimation and hypothesis testing. There are three main aims of this class:

to learn the language of probability (talk)
to improve your statistical intuition (think)
to understand the mathematical machinery necessary to express and prove stochastic concepts (reason)

And we will cover three broad topics:

basic tools of probability, the mathematics of chance
distributions and random variables
statistical methodologies connecting probability with data: estimation and testing

Textbook

Textbook: Mathematical Statistics with Applications by Ramachandran and Tsokos. If you buy it using this link to amazon I'll contribute my amazon associates earnings to a class party at the end of the semester.

Assessment

10x weekly homework = 40%.

Your lowest grade will be dropped, so late homeworks will only be accepted under exceptional circumstances. Most homeworks will be graded out of 10, with the possiblity of 2 points of extra credit. This will allow you to make up missed points, but your overall homework grade will be capped at 100%. Graders have the option to subtract one point if your assignment is overly messy or not stapled.

You may co-operate on homework but you must submit your own assignment that reflects your own thinking, work and organisation. To check if you homework passes this standard, imagine I asked you to explain your reasoning for each problem - you should be able to do so with ease. All homeworks are to be pledged and signed.
7x in-class quizes = 10%

These quizes will take 5-10 minutes to complete and will be trivial if you've done the reading. The point of them is to encourage you to do the reading and to show up for class - these are both habits that are highly correlated with success.
2x mid-term exams = 20%

See below for dates.
1x comprehensive final exam = 30%

Grading scale

90 - 100 = A
75 - 89 = B
55 - 74 = C
30 - 54 = D
0 - 29 = F

Classroom culture

If you would rather be sleeping, reading the newspaper, listening to your ipod or shopping for shoes on the internet, I’d suggest that you do that somewhere much more comfortable than the classroom. Online poker is strongly discouraged.

Please make sure to bring a calculator along to class.

Disability policy

If you have a documented disability that will impact your work in this class, please contact me to discuss your needs. Additionally, you will need to register with the Disability Support Services Office in the Ley Student Center.

Tentative timetable

Probability

Jan 12. Introduction to probability and statistics.
Jan 14. Probability mass functions and counting.
Jan 19. Conditional probability
Jan 21. Independence and Bayes theorem

Discrete distributions

Jan 26. Introduction to random variables. Probability mass functions. Expectation.
Jan 28. Mean & variance.
Feb 2. Bernoulli & binomial. Moment generating function. Poisson.
Feb 4. Continuous random variables. Expectation. Uniform distribution.

Continuous distributions

Feb 9. Exponential & gamma distributions.
Feb 11. Transformations.
Feb 16. Connections between distributions.
Feb 18. EXAM

Multivariate distributions

Feb 23. Introduction to bivariate distributions
Feb 25. 2d random variables. Marginal and conditional distributions.
Mar 2. Spring break.
Mar 4. Spring break
Mar 9. 2d transformations.
Mar 11. Bivariate change of variables.

Inference

Mar 16. Sequences.
Mar 18. Sampling distributions: introduction.
Mar 23. Sampling distribution: mean and variance.
Mar 25. Introduction to inference
Mar 30. EXAM

Estimation

Apr 1. Midterm recess
Apr 6. Maximum likelihood, method of moments.
Apr 8. Point estimation and standard errors.
Apr 13. Confidence intervals.

Testing

Apr 15. Testing basics.
Apr 20. Randomisation tests.
Apr 22. Fin.