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


The recommended textbook is 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. Otherwise I encourage you to buy second hand and international editions.

The book is not absolutely required, but it will provide a backup for what you learn in class.

Mathematical background

I expect you to be familiar with basic algebra, calculus, and set theory. This quick reference sheet outlines my expectations. I don’t guarantee it’s exhaustive, but if it all looks familiar then you shouldn’t have any problems with the maths in the course.

We will use wolfram alpha extensively in class, and I expect you will also use it in your homeworks.


  • 10 weekly homeworks + 3 one page essays = 60%.

    Lowest two grades dropped.

    Weekly homeworks due are 4pm Thursday. If handed in by 5pm Friday, you will get a 10% penalty. If large numbers of homeworks are turned in late, the penalty may be increased. Homeworks handed in after 5pm Friday will not be accepted. Exceptionally messy, hard to read or unstapled homeworks will receive a 25% penalty. This penalty can be lifted by turning in a cleanly written copy, or a photo of you holding a stapler and box of staples.

    Homework 0 will be counted as half a normal homework, and will not be included in the dropped grades.

    One page essays are due one week following each test.

    You may co-operate on homework but you must submit your own assignment that reflects your own thinking, work and organisation. To check if your homework meets 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 considered to be pledged.

    Bonus points will be available for some homeworks, but your final homework will not contribute more than 60% to you final grade.

  • 2 take-home tests = 20%

    When taking a test, you must work by yourself, and not use any materials apart from the permitted one page (two sides) of notes. All tests must be pledged and signed.

  • 1 comprehensive take-home final exam = 20%

Grading scale

  • 90 - 100 = A
  • 80 - 89 = B
  • 65 - 79 = C
  • 50 - 64 = D
  • 0 - 49 = F

You will receive an F if you get less than 50% in any assessment category (homeworks, tests and final). Plusses and minuses will be awarded at my discretion. A+s will be awarded to the most exceptional students.

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


  • Jan 10. Introduction to probability and statistics.
  • Jan 12. Probability mass functions and counting.
  • Jan 17. Conditional probability
  • Jan 19. Independence and Bayes theorem

Discrete distributions

  • Jan 24. Introduction to random variables. Probability mass functions. Expectation.
  • Jan 26. Mean & variance.
  • Jan 31. Bernoulli & binomial. Moment generating function.
  • Feb 2. Poisson distribution. Connections between discrete distributions.

Continuous distributions

  • Feb 7. Continuous random variables. Expectation. Uniform distribution.
  • Feb 9. Exponential & gamma distributions.
  • Feb 14. Transformations.
  • Feb 16. Connections between distributions.
  • Feb 20. Test

Multivariate distributions

  • Feb 21. Introduction to bivariate distributions
  • Feb 23. 2d random variables. Marginal and conditional distributions.
  • Mar 1. Spring break.
  • Mar 3. Spring break.
  • Mar 6. 2d transformations.
  • Mar 8. Bivariate change of variables.


  • Mar 13. Sequences.
  • Mar 15. Sampling distributions: introduction.
  • Mar 20. Sampling distribution: mean and variance.
  • Mar 22. Mid term recess.
  • Mar 26. Test.

Inference: Estimation

  • Mar 27. Introduction to inference
  • Mar 29. Maximum likelihood
  • Apr 3. More maximum likelihood, method of moments.
  • Apr 5. Point estimation and standard errors.
  • Apr 10. Confidence intervals.

Inference: Testing

  • Apr 12. Testing basics.
  • Apr 17. Randomisation tests.
  • Apr 19. Fin.