Exercises for Statistical Theory and Modelling, 7.5 hp

AI generated image of a mixture distribution

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. BLprequel X.Y.Z means Chapter X, Section Y, Problem Z in the Bayesian prequel book.

Exercise problems

Exercise 1 - Differentiation, optimization and integration.
BLprequel 1.14.1, 1.14.3, 1.14.4, 1.14.7, 1.14.11, 1.14.12, 1.15.1, 1.15.2, 1.15.4, 1.16.1, 1.16.3, 1.16.4, 1.16.8, 1.16.9.

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

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

Exercise 4 - Joint and conditional distributions.
Problems MSA: 5.7, 5.25, 5.61, 5.76, 5.89, 5.91, 5.114 (hint: these are well-known distributions)
Problems BLprequel: 7.8.1-7.8.5

Exercise 5 - Transformation of variables. Law of large numbers. Central limit theorem.
MSA 6.4a, 6.24, 6.23a-b, 6.12 (use the transformation method), 6.28.
Interactive problems: W5.1, W5.2

Exercise 6 - Maximum likelihood estimation.
MSA: 9.80, 9.97b.
BLprequel: 8.3.1, 8.3.2, 8.5.1, 8.5.2.

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

Exercise 8 - Test Exam
An exam from last year will be solved (available later on Athena).