Statistics

  1. Probability Theory
    1. Fundamental Concepts
      1. Experiment
        1. Random Experiments
          1. Deterministic vs. Random
          2. Outcome
            1. Simple Outcomes
              1. Compound Outcomes
              2. Event
                1. Simple Events
                  1. Compound Events
                    1. Complementary Events
                    2. Sample Space
                      1. Listing Outcomes
                        1. Finite vs. Infinite Sample Spaces
                          1. Event Notation
                            1. Venn Diagrams
                            2. Probability Definitions
                              1. Classical Probability
                                1. Equally Likely Outcomes
                                  1. Limitations
                                  2. Empirical Probability
                                    1. Relative Frequency
                                      1. Law of Large Numbers
                                      2. Subjective Probability
                                        1. Personal Beliefs
                                          1. Expert Opinions
                                      3. Rules of Probability
                                        1. Basic Properties
                                          1. Probability Range
                                            1. Certainty and Impossibility
                                              1. Complement Rule
                                              2. The Addition Rule
                                                1. Mutually Exclusive Events
                                                  1. Non-Mutually Exclusive Events
                                                    1. General Addition Rule
                                                    2. The Multiplication Rule
                                                      1. Independent Events
                                                        1. Dependent Events
                                                          1. General Multiplication Rule
                                                          2. Conditional Probability
                                                            1. Calculation
                                                              1. Independence Testing
                                                              2. Bayes' Theorem
                                                                1. Formula
                                                                  1. Prior and Posterior Probabilities
                                                                    1. Tree Diagrams
                                                                  2. Counting Techniques
                                                                    1. Fundamental Counting Principle
                                                                      1. Multiplication Principle
                                                                      2. Permutations
                                                                        1. Without Repetition
                                                                          1. With Repetition
                                                                            1. Circular Permutations
                                                                              1. Formula Applications
                                                                              2. Combinations
                                                                                1. Without Repetition
                                                                                  1. With Repetition
                                                                                    1. Pascal's Triangle
                                                                                      1. Formula Applications

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                                                                                  3. Descriptive Statistics: Organizing and Summarizing Data

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                                                                                  5. Probability Distributions