## Preliminary curriculum (there can be changes)

The curriculum consists of

• Chapter 1: Introduction to probability theory assumed to be known
• Chapter 2: Random variables assumed to be known
• Chapter 3: Conditional probability and condititional expectation, 3.1 - 3.5, 3.6.3
• IMPORTANT PARTS :
1. 3.1,
2. 3.2 first part, including example 3.1
3. 3.3 first part, including example 2.5
4. 3.4 first part (until example 3.11) + example 3.16 (quick-sort algorithm) + 3.4.1 (until example 3.20)
5. 3.5 first part, including example 3.21 + Example 3.25 (Best prize)
6. 3.6.3 p 141-145
• Chapter 4: Markov chains, 4.1 - 4.9
• IMPORTANT PARTS :
1. 4.1,
2. 4.2,
3. 4.3 all (except example 4.19)
4. 4.4 all (except example 4.23, 4.24, 4.25 and 4.27, and Prop 4.6)
5. 4.5 first part, 4.5.1
6. 4.6 all
7. 4.7 all
8. 4.8 all (except example 4.37 and 4.38)
9. 4.9 all (except example 4.40 and 4.41)
• Chapter 5: The Exponential Distribution and the Poisson Process, 5.1 - 5.3
1. 5.1 all
2. 5.2 all (except example 5.6, 5.7, 5.9, 5.10 and 5.11)
3. 5.3 all (except example 5.18, 5.19, 5.20, 5.22, 5.23)
4. 5.4 Basic properties of Non-homogeneous Poisson process (5.4.1), compound process (5.4.2) and mixed processes (5.4.3).
• Chapter 6: Continuous-time Markov chains, 6.1 - 6.5
1. 6.1 all
2. 6.2 all (except example 6.1)
3. 6.3 all
4. 6.4 all
5. 6.5 all (except example 6.15-16)
• Chapter 8: Queueing theory,
1. 8.1 all
2. 8.2 all
3. 8.3 8.3.1 (until Example 8.4), 8.3.2 (until Ex 8.5 finished), 8.3.4 (all).
4. 8.5 (all)
5. 8.9.1, 8.9.2 (all)
• Chapter 10: Brownian motion,
1. 10.1 - 10.3 (all),
2. 10.4.3 (until eq 10.12),
3. 10.7 (until Prop 10.1).

in Ross, S. (2014). Introduction to Probability Models, 11th edn, Academic Press" which is also available freely to NTNU students as an ebook here.

Everything covered in the lectures, project and exercises is also part of the curriculum.