Exercises for Statistical Theory and Modelling, 7.5 hp

The course builds on mathematical and statistical concepts that you need to train on by solving many exercises.

Schedule

The course schedule can be found on TimeEdit.

Literature - problems

The exercise numbers below uses the numbering in the course book (denoted by MSA below):
Wackerley, Mendenhall and Scheaffer (2021). Mathematical Statistics with Applications, 7th edition, Cengage.

Note: Problems in the book marked with Applet exercises should be solved with the Observable widgets for the course.

The BLprequel listed below are section numbers from a book Bayesian Learning - the prequel that I have started writing for this course.

Exercise problems

Exercise 1 - Differentiation, optimization and integration.
Problems: Exercises from the BLprequel book, Sections 1.14 (Differentiation), 1.15 (Integration) and 1.16 (Function optimization).

Exercise 2 - Discrete random variables.
Problems: MSA 3.1, 3.9, 3.12, 3.33, 3.39, 3.40, 3.92, 3.93, 3.94, 3.122, 3.124, 3.125, 3.167

Exercise 3 - Continuous random variables.
Problems: MSA 4.9, 4.11, 4.12, 4.14, 4.20, 4.30, 4.71, 4.88, 4.105a. 4.109, 4.110, 4.114a-d, 4.128
Interactive problems: W4.1, W4.2

Exercise 4 - Joint and conditional distributions.
Problems: MSA 5.4, 5.16, 5.5, 5.7, 5.25, 5.36, 5.48, 5.60, 5.61, 5.76, 5.89, 5.91, 5.103, 5.114 (hint: these are well-known distributions), 5.136, 5.141.

Exercise 5 - Transformation of variables. Law of large numbers. Central limit theorem.
Problems: MSA 6.4a, 6.12, 6.24, 6.26.
Interactive problems: W5.1, W5.2

Exercise 6 - Maximum likelihood estimation.
Problems: MSA 9.80, 9.81, 9.85a, 9.97b, 9.98, 9.103.

Exercise 7 - Linear algebra. Linear regression in matrix form.
Problems: MSA 5.131a, 11.66, 11.68 (use R to compute the matrix inverse)

Exercise 8 - Time series
Problems: MSA X.X, Y.Y, …