## 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 :
- 3.1,
- 3.2 first part, including example 3.1
- 3.3 first part, including example 2.5
- 3.4 first part (until example 3.11) + example 3.16 (quick-sort algorithm) + 3.4.1 (until example 3.20)
- 3.5 first part, including example 3.21 + Example 3.25 (Best prize)
- 3.6.3 p 141-145

**Chapter 4: Markov chains**, 4.1 - 4.9- IMPORTANT PARTS :
- 4.1,
- 4.2,
- 4.3 all (except example 4.19)
- 4.4 all (except example 4.23, 4.24, 4.25 and 4.27, and Prop 4.6)
- 4.5 first part, 4.5.1
- 4.6 all
- 4.7 all
- 4.8 all (except example 4.37 and 4.38)
- 4.9 all (except example 4.40 and 4.41)

**Chapter 5: The Exponential Distribution and the Poisson Process**, 5.1 - 5.3- 5.1 all
- 5.2 all (except example 5.6, 5.7, 5.9, 5.10 and 5.11)
- 5.3 all (except example 5.18, 5.19, 5.20, 5.22, 5.23)
- 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- 6.1 all
- 6.2 all (except example 6.1)
- 6.3 all
- 6.4 all
- 6.5 all (except example 6.15-16)

**Chapter 8: Queueing theory**,- 8.1 all
- 8.2 all
- 8.3 8.3.1 (until Example 8.4), 8.3.2 (until Ex 8.5 finished), 8.3.4 (all).
- 8.5 (all)
- 8.9.1, 8.9.2 (all)

**Chapter 10: Brownian motion**,- 10.1 - 10.3 (all),
- 10.4.3 (until eq 10.12),
- 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.**