UsefulLinks
Statistics
Statistics with R
1. Introduction to R and Statistical Computing
2. R Fundamentals and Basic Operations
3. R Package System
4. R Data Structures
5. Data Import and Export
6. Data Cleaning and Preprocessing
7. Data Manipulation with dplyr
8. Descriptive Statistics
9. Data Visualization Fundamentals
10. Advanced Data Visualization with ggplot2
11. Probability Theory
12. Probability Distributions
13. Sampling and Sampling Distributions
14. Statistical Inference Foundations
15. Hypothesis Testing Framework
16. One-Sample Tests
17. Two-Sample Tests
18. Chi-squared Tests
19. Analysis of Variance (ANOVA)
20. Correlation Analysis
21. Simple Linear Regression
22. Regression Diagnostics
23. Multiple Linear Regression
24. Generalized Linear Models
25. Nonparametric Statistics
26. Introduction to Time Series Analysis
27. Introduction to Machine Learning
28. Reproducible Research
29. Statistical Computing Best Practices
11.
Probability Theory
11.1.
Fundamental Concepts
11.1.1.
Random Experiments
11.1.2.
Sample Spaces
11.1.3.
Events
11.1.4.
Probability Definitions
11.1.4.1.
Classical Probability
11.1.4.2.
Relative Frequency
11.1.4.3.
Subjective Probability
11.2.
Probability Rules
11.2.1.
Addition Rule
11.2.2.
Multiplication Rule
11.2.3.
Complement Rule
11.2.4.
Conditional Probability
11.2.5.
Independence
11.2.6.
Mutually Exclusive Events
11.3.
Bayes' Theorem
11.3.1.
Theorem Statement
11.3.2.
Prior and Posterior Probabilities
11.4.
Counting Principles
11.4.1.
Permutations
11.4.2.
Combinations
11.4.3.
Factorial Notation
11.5.
Random Variables
11.5.1.
Definition and Types
11.5.2.
Discrete Random Variables
11.5.3.
Continuous Random Variables
11.5.4.
Probability Functions
11.5.4.1.
Probability Mass Functions
11.5.4.2.
Probability Density Functions
11.5.4.3.
Cumulative Distribution Functions
11.6.
Expected Value and Variance
11.6.1.
Expected Value
11.6.2.
Variance and Standard Deviation
11.6.3.
Properties of Expected Value
11.6.4.
Properties of Variance
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12. Probability Distributions