Statistics

  1. Probability Distributions
    1. Random Variables
      1. Types of Random Variables
        1. Discrete Random Variables
          1. Probability Mass Function (PMF)
            1. Properties of PMF
              1. Expected Value
                1. Variance
                2. Continuous Random Variables
                  1. Probability Density Function (PDF)
                    1. Properties of PDF
                      1. Cumulative Distribution Function (CDF)
                        1. Expected Value
                          1. Variance
                        2. Discrete Probability Distributions
                          1. Binomial Distribution
                            1. Conditions
                              1. Probability Formula
                                1. Mean and Variance
                                  1. Normal Approximation
                                  2. Poisson Distribution
                                    1. Conditions
                                      1. Probability Formula
                                        1. Mean and Variance
                                          1. Poisson Process
                                          2. Hypergeometric Distribution
                                            1. Conditions
                                              1. Probability Formula
                                                1. Differences from Binomial
                                                2. Geometric Distribution
                                                  1. Conditions
                                                    1. Probability Formula
                                                      1. Mean and Variance
                                                        1. Memoryless Property
                                                        2. Negative Binomial Distribution
                                                          1. Conditions
                                                        3. Continuous Probability Distributions
                                                          1. The Normal Distribution
                                                            1. Properties of the Normal Curve
                                                              1. Bell Shape
                                                                1. Symmetry
                                                                  1. Asymptotic Tails
                                                                  2. Parameters
                                                                    1. Mean (μ)
                                                                      1. Standard Deviation (σ)
                                                                      2. Empirical Rule (68-95-99.7 Rule)
                                                                        1. The Standard Normal Distribution (Z-distribution)
                                                                          1. Standardization
                                                                            1. Z-tables
                                                                              1. Probability Calculations
                                                                            2. The Uniform Distribution
                                                                              1. Continuous Uniform
                                                                                1. Parameters
                                                                                2. The Exponential Distribution
                                                                                  1. Parameters
                                                                                    1. Memoryless Property
                                                                                    2. The t-Distribution
                                                                                      1. Degrees of Freedom
                                                                                        1. Comparison with Normal
                                                                                        2. The Chi-Square Distribution
                                                                                          1. Degrees of Freedom
                                                                                          2. The F-Distribution
                                                                                            1. Parameters
                                                                                          3. The Central Limit Theorem
                                                                                            1. Statement and Importance
                                                                                              1. Conditions
                                                                                                1. Sample Size Requirements
                                                                                                  1. Applications in Sampling
                                                                                                    1. Demonstration with Examples

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                                                                                                  4. Probability Theory

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                                                                                                  6. Sampling Distributions