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.
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
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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)
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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
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