Advanced Mathematics for Electrical Engineers B -- fall semester 2014
This web page is ONLY about the first, "Stochastics" half of the semester, taught by Imre Péter Tóth and Gusztáv Morvai.


Here are the results of the homeworks, midterms and exams.

This was the fourth exam, and here are the solutions.
This was the third exam. Sorry, there is an error in the first exercise. The correct question should be: Give a large deviation estimate for the probability that the average of the results reaches 2.6
This was the second exam.
The first exam was exactly the same as the 2nd resit midterm.
This was the 2nd resit of the midterm.
This was the resit of the midterm.
This was the midterm, and here are the solutions. Of course, there can be errors in the solutions.

The precise place of all the exams that are left: room E1B.

Timing of the exams: You should first take the half-exam of Dávid Szeszlér, and after that, come to the written second part at 13:00.

There will be a pre-exam question and answer session

• On the 5th of January 2015, from 12:30 in room H663.
• On the 12th of January 2015, from 08:45 in room H607.
• On the 19th of January 2015, from 16:00 in room H46.
• On the 26th of January 2015, from 13:00 in room H607.

Material of the exam: The exam will cover only those topics which I managed to cover on the lectures. This means that there will be no questions about continuous time Markov chains, and there will be no questions about Statistics.
On the exam I plan to have 4 exercises for 60 minutes. However, it is possible that time limitations will only allow 3 exercises for 45 minutes. Expect something similar to last year's exam, which is here. (Of course, with the note that there will be no statistics.)

This was the midterm, and here are the solutions. Of course, there can be errors in the solutions.

Homeworks here.

Solutions of the Homeworks here.

Exercise sheets and midterm exams from earlier years here.

Subject code: BMETE90MX38
Course code for the lecture: A0
Course code for the tutorial: A1
Official data sheet of the course: TE90MX38
Lectures: Wednesday 8:15-10:00, room E401 and Wednesday 10:15-12:00, room IB138
Tutorial: Monday 12:00-13:30, room H-601 the real time and place differs from those published in the Neptun system.
Lecturer: Imre Péter Tóth for the first half of the semester (weeks 1-7), after that Dávid Szeszlér.
Tutor: Gusztáv Morvai for the first half of the semester (weeks 1.-7), after that ??
This web page is ONLY about the first half of the semester, taught by Imre Péter Tóth and Gusztáv Morvai, named "Stochastics 2".
Schedule (planned), "Stochastics 2" part:

week #	when	topic	remark
week 1	2014.09.08-12	Repetition
week 2	2014.09.15-19	Repetition	no lectures on Wednesday (sports day)
week 3	2014.09.22-26	Generating functions and their applications
week 4	2014.09.29-10.03	Large deviations
week 5	2014.10.06-10	Markov chains in discrete time
week 6	2014.10.13-17	Markov chains in continuous time
week 7	2014.10.20-24	Basics of Statistics

Suggested literature:
[Feller I]: W. Feller: An Introduction to probability Theory. Vol 1, 3rd edition (Wiley, 1968)
[Feller II]: W. Feller: An Introduction to probability Theory. Vol 2, 3rd edition (Wiley, 1971)

Some details of where to find the material of the course:

• Conditional probability: [Feller I], sections V.1,3 (Bayes' Rule: equation (2.12) )
• Binomial and Poisson distribution: [Feller I], sections VI.1,2,5,6,7
• Expectation: [Feller I], section IX.1,2,3,4
• Branching processes: [Feller I], section XII.1,3,4
• Central limit theorem: [Feller II], section VIII.4

Midterm exams:
Midterm: 2014.10.29. Wednesday 18.00 - 20.00, room H-601. The real place differs from that published in the Neptun system.
Midterm resit: 2014.12.12, Friday 10:00 - 12:00, room E1B.

Grading rules:
50-50 points can be reached from each half-course. Within this, from the "Stochastics 2" half-course

• the 5 weekly hand-in homeworks are worth 5 points,
• the midterm exam is worth 20 points,
• the final exam is worth 25 points.

Handing in the homeworks is not compulsory, but strongly recommended. Those who have a signature from an earlier semester, can choose if they wish to write the midterm (which they may fail), or not to write it, so the signature is counted as 8 points. The condition for getting a signature is

• reaching at least 40% (8 points) on the midterm, and
• reaching at least 40% (10 points) from the midterm and the homeworks together, and
• reaching the minimum requirements of the other half-course.

To pass the course, one needs to get at least 40% (10 points) of the final exam of this half-course and 40% of the points from each half-course separately (20-20 points).

After this, the final grade is calculated from the total score (out of 100) as follows:

0-39 points	1
40-54 points	2
55-69 points	3
70-84 points	4
85-100 points	5

During the midterm, students may use

• a not too clever calculator,
• formula sheet of statistical tests,
• table of normal, Student t and Chi-square distributions,
• (initially empty) paper, pens, food and drink,
• an ID with photo,
• nothing else.

---

Detailed list of topics:

---

Week 1: Repetition

• conditional probability, independence, law of total probability
• One-dimensional random variables, weight function (= discrete probability distribution), density function, distribution function
• important distributions: discrete uniform, Bernoulli, binomial, geometric, Poisson, uniform on an interval, exponential, normal
• expectation, variance
• multi-dimensional random variables
• conditional distribution, law of total expectation
• expectation vector, covariance matrix, correlation

Recommended reading: Sheldon Ross: Introduction to probability models (Academic Press, Elsevier 2006) Chapter 1 and sections 2.1-2.5
Recommended practice exercises from earlier years here (from Balázs Székely).

---