# Stochastics for MSc students of Electrical Engineering

Fall semester 2021
Course code: BMETE90MX55
No. of credits: 3

Classes:
• Tuesdays 8:30-10:00, room E402
• Wednesdays 12:15-13:45 on even weeks (Week 2 is 15 Sept.), room E304-305

• You can contact me by e-mail: pollux@math.bme.hu

Office hours: Tuesdays 14:00-15:00, room IB115 (building I).

Requirements and general information

Lecture slides (available as the semester progresses):
• 01 - Basic Probability 1.pdf
• 02 - Basic Probability 2.pdf, lecture recording
• 03 - Generating Functions.pdf
• 04 - Branching Processes.pdf
• 05 - Poisson Processes.pdf
• 06 - Concentration Theorems.pdf
• 07 - Markov Chains.pdf
• 08 - Continuous Time Markov Chains.pdf
• 09 - Statistics I.pdf
• 10 - Statistics II.pdf
• 11 - Statistics III.pdf

• Materials that can (and should) be used during the semester and the midterm tests:
• Special distributions (pdf)
• Statistical tests (pdf)
• Statistical tables (z, t, chi-square) (pdf)

• Problem sheets:
• 1. Basic probability problems 1 (pdf), some results (pdf)
• 2. Basic probability problems 2 (pdf), some results (pdf)
• 3. Generating function problems (pdf), some results (pdf)
• 4. Branching process problems (pdf), some results (pdf), even more results (pdf)
• 5. Poisson process problems (pdf), some results (pdf)
• 6. Concentration theorems problems (pdf), some results (pdf)
• Sample problems for Midterm test 1 (pdf), solutions (pdf)
• 7. Markov chains problems (pdf), some results (pdf)
• 8. Continuous time Markov chains problems (pdf), extra problems, some results (pdf)
• 9. Statistics I problems (pdf)
• 10. Statistics II problems (pdf)
• 11. Statistics III problems (pdf)

• For specific topics, I recommend further reading (see the list of books below). I recommend Kulkarni wherever applicable. In general, the other books are more detailed and more theoretical than expected; focus on definitions, main theorems and examples rather than on proofs and lemmas.
• Basic probability: Durrett (Probability) chapters 1.1, 1.2, 1.3, 1.6, 2.1 (pages 37-38)
• Probability generating function: Grinstead-Snell 10.1 (from subsection Ordinary Generating Function)
• Poisson process: Durrett (Stochastic Processes) 2.2, Kulkarni 3
• Concentration theorems: Durrett (Probability) 2.4, 3.4.1, 3.4.4, 2.6
• Discrete time Markov chains: Durrett (Probability) 6.1-6.7, Ross 4.1-4.6, Kulkarni 2.1-2.6
• Continuous time Markov chains: Ross 6.1-6.5, Kulkarni 4.1-4.7, 6.3