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Probability and Statistics, Events, Random variables, Distributions, Moments, Main Limit Theorems, Hypothesis, Regression and more. Statistical Computing and Graphics with R.

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Empirical Methods and Statistics

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Тhis repository contains notes on statistics and empirical methods from the Sofia University course.
It is intended for beginners, who are interested in statistics and wants to develop in this field.

If you have troubles understanding the concepts or you have a suggestion please submit an issue.
I'm not committing to an answer, but these issues will be open and someone else may feel free to help.

Lectures

N date pdf N date pdf N date pdf
01 2020-10-01 SEM L01 06 2020-11-05 SEM L06 11 2020-12-10 SEM L11
02 2020-10-08 SEM L02 07 2020-11-12 SEM L07 12 2020-12-17 SEM L12
03 2020-10-15 SEM L03 08 2020-11-19 SEM L08 13 2020-01-07 SEM L13
04 2020-10-22 SEM L04 09 2020-11-26 SEM L09 14 2020-01-14 SEM L14
05 2020-10-29 SEM L05 10 2020-12-03 SEM L10 15 2020-01-21 SEM L15

Exercises

Week N Statistics and Empirical Methods
Practical Exercises		 Statistical Computing
Data Testing and Graphics with R
01 1.1. Combinatorics – Problems
1.2. Combinatorics – Solutions 1-9
1.3. Combinatorics – Solutions 10		 1.0. Introduction
1.1. Basic Syntax
1.2. Data Types
1.3. Data Structures
1.4. Missing Data
1.5. Packages
1.6. Reading Data
1.7. Descriptive Statistics
1.8. Examples
1.9. Verzani Problem Set
1.10. Vectors (Moodle Tasks)
1.11. Vectors (Moodle Tasks Solutions)
02 2.1. Combinatorics part 2 – Problems
2.2. Combinatorics part 2 – Solutions 1-7
2.3. Probabilities - Problems		 2.1. Univariate Data
2.2. Verzani Problem Set
2.3. Moodle Tasks
2.4. Moodle Tasks Solutions
03 3.1. Conditional Probabilities, Independent Events – Problems
3.2. Conditional Probabilities, Independent Events – Solutions
3.3. Exercise 3 – Problems
3.4. Exercise 3 – Solutions 1-7		 3.1. Bivariate Data
3.2. Verzani Problem Set
3.3. Moodle Tasks
3.4. Moodle Tasks Solutions
04 4.1. Conditional Probabilities bis – Problems
4.2. Conditional Probabilities – Solutions 5-8
4.3. FMI – PTMS 1-2-3 Solutions
4.4. FMI-PTMS 4 – Problems
4.4. FMI-PTMS 4 – Hints and Solutions
4.6. FMI-PTMS 4 – Solutions		 4.1. Multivariate Data
4.2. Moodle Tasks
05 5.1. Bayes Law, Geometric Probability – Problems
5.2. Bayes Law, Geometric Probability – Solutions 1-7
5.2. Bayes' Law, Geometric Probability – Solutions 8-9
5.3. Bayes Law, Geometric Probability. Hints and Solutions
5.4. FMI – PTMS 5 – Problems
5.5. FMI - PTMS 5 – Solutions
5.6. FMI - PTMS 5 – Detailed Solutions
5.7. Solutions with Drawings		 -
06 6.1. Geometric Probability. Discrete Random Variables.
6.2. Discrete Random Variables – Problems
6.3. Discrete Random Variables – Solutions		 6.1. Random Data (Variables)
6.2. Verzani Problem Set
6.3. Moodle – Discrete Random Variables – Problems
6.4. Moodle – Discrete Random Variables – Solutions
6.5. Moodle – Continuous Random Variables – Problems
6.6. Moodle – Continuous Random Variables – Solutions
07 7.1. Discrete Random Variables part 2
7.1. Discrete Random Variables – Problems
7.3. Discrete Random Variables – Solutions
7.4. First Control test Preparation (Past Problems and Solutions)		 -
08 8.1. Discrete Random Variables part 3
8.2. FMI PTMS 8 – Problems
8.2. FMI PTMS 8 – Solutions		 8.1. Limit Theorems. Convergence. Normal Distribution Tests
09 9.1. Discrete Random Variables part 4
9.2. FMI – PTMS 9 – Problems
9.3. FMI – PTMS 9 – Solutions
9.4. Control Test 1, variant 1, groups 1-3 – Problems
9.5. Control Test 1, variant 1, groups 1-3 – Detailed Solutions
9.6. Control Test 1, variant 2, групи 1-3 – Problems (similar)
9.7. Control Test 1, groups 4-5 – Problems
9.8. Control Test 1, groups 4-5 – Solutions		 9.1. Confidence Interval Estimation
9.2. Verzani Problem Set
9.3. Moodle – Confidence Intervals – Problems
9.3. Moodle – Confidence Intervals – Solutions
10 10.1. Continuous Random Variables, groups 4-5, part 1
10.2. FMI – PTMS 10 – Problems
10.3. FMI – PTMS 10 – Solutions		 10.1. Hypothesis Testing
10.2. Verzani Problem Set
11 11.1. Continuous Random Variables, groups 4-5, part 2
11.2. FMI PTMS 12 – Problems
11.3. FMI PTMS 12 – Solutions		 11.1. Two-sample Hypothesis Testing
11.2. Verzani Problem Set
11.3. Moodle – Hypothesis testing (two samples) – Problems
11.3. Moodle – Hypothesis testing (two samples) – Solutions
12 12.1. Continuous Random Variables part 3 12.1. Chi-square Tests
12.2. Verzani Problem Set
13 13.1. Continuous Random Variables part 4
13.2. Continuous Random Variables, FMI – PTMS 12-14		 13.1. Regression Analysis
13.2. Verzani Problem Set
14 14.1. Continuous Random Variables 5
14.2. FMI PTMS 12-14 – Problems
14.3. FMI PTMS 12-14 – Solutions		 14.1. Multiple Linear Regression
14.2. Verzani Problem Set
15 15.1. Control Test 2 Preparation
15.2. Control Test 2, groups 1-3 – Problems
15.3. Control Test 2, groups 1-3 – Detailed Solutions
15.4. Control Test 2, groups 4-5 – Problems
15.5. Control Test 2, groups 4-5 – Solutions		 15.1. Analysis of Variance (ANOVA)
15.2. Verzani Problem Set

Exams and Preparation for Exams

date pdf
- Exam Preparation – Problems
Exam Preparation – Solutions
2021-01-27 SEM Final Exam – Problems and Solutions
2021-02-03 SEM Final Exam – Problems
Sem Final Exam – Solutions
Detailed Solutions for Selected Exam Problems: 4, 6, 7, 9

Homeworks

groups pdf
1-3 SEM HW groups 1-3 SE – Problems
SEM HW groups 1-3 SE – Solutions
4-5 SEM HW groups 4-5 SE – Problems

Additional Problems

N Problems
01 Crux Mathematicorum VOLUME 42, No. 6, June 2017, page 11 (Geometric Probability)
02 Crux Mathematicorum VOLUME 47, No. 1, January 2021, pages 13-18 (Games, Geometric Probability)
03 Number of sixes probability (Chebyshev & CLT)
04 Fair Die Distribution
05 2X-3Y
06 Coprime Natural Numbers Probability
07 Deck of Cards Questions
08 Basic Randomization
09 x/y closer to even integer probability

Interview Tasks

Problems Solutions
Interview Problems (Game-Math Designer, Quant Developer, Mathematician) Solutions

References:

  • [1] Empirical Methods and Statistics lecture notes @ FMI - Sofia University, Software Engineering, lecturer: Mladen Savov
  • [2] Probabilities Theory - Exercises, Emil Kamenov, Miroslav Stoenchev
  • [3] Monika Peteva Petkova's notes on R programming language
  • [4] Martin Minchev's notes on Probabilities and Statistics
  • [5] SimpleR - Using R for Introductory Statistics, John Verzani
  • [6] Crux mathematicorum, Canadian mathematical forum
  • [7] Probability and Random Processes, Geoffrey R. Grimmett and Davis R. Stirzaker, Third Edition
  • [8] One Thousand Exercises in probability, Geoffrey R. Grimmett and Davis R. Stirzaker
  • [9] Dobromir Pavlov Kralchev's notes on Combinatorics and Generating functions
  • [10] William Lowell Putnam Mathematical Competition
  • [11] 102 Combinatorial Problems, Book by Titu Andreescu and Zuming Feng
  • [12] My personal notes, solutions and opiniоnated approaches for problem solving

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Probability and Statistics, Events, Random variables, Distributions, Moments, Main Limit Theorems, Hypothesis, Regression and more. Statistical Computing and Graphics with R.

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