Some relevant problems for the exam

As it was already mentioned, there will be 3 problems on the exam (which cover 3 major topics of the course) - the structure of the exam will be approximately the same as the one of the trial exam posted some time ago.

However, if one wants to prepare even better, one can solve the following:

Problem 1:  Problem 1 of Exam 2021, Problems 1 and 2 of Exam 2020, Problem 1 of Exam 2018, Problems 1 and 2 of Exam 2017, Problem 1 of Exam 2016, Problem 1 of Exam 2015; also it is heavily recommended to take a closer look at Lecture 3 and Lecture 10 (mean time spent in transient states).

Problem 2: Problem 2 of Exam 2018, Problem 3 of Exam 2017, Exercises from the textbook 5.37, 5.39 and 5.78; also it is recommended to remember by heart the density and the expectation of the Gamma distribution, its connection to exponential distribution and the Poisson process (see Lecture 19 in general and Example 5.13) as well as all formulas related to the Poisson distribution.

Problem 3: Problem 3 of Exam 2021, Problem 4 of Exam 2020, Problem 4 of Exam 2017, Problem 2 of Exam 2016, Problem 2 of Exam 2015, Exercises from the textbook 6.8, 6.10; also it is heavily recommended to know the theory (including the proofs!) of Lecture 26 and Lecture 28 (note that there are some changes in the lecture notes since I spotted a typo in Example 6.12).