Empirical Methods and Statistics

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
10	Dice process

Additional Material

N	Links
01	Central Limit Theorem
02	Berry-Essen Bounds (Analysing the speed of convergence of CLT)
03	Radon Nikodym

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