Probability and Statistics

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Probability and Statistics release 25.63

FULL VERSION
CONTENTS

Part I Probability
- Counting Principles and Probability
  - Counting Principles
    - Permutations
      - Permutations of n Elements
      - Permutations of n Elements Taken r at a Time
      - Distinguishable Permutations
    - Combinations
    - Fundamental Counting Principles
  - Probability
    - Basic Probability Concepts
    - Venn Diagram
    - Conditional Probability and Multiplication Theorem
    - Addition Theorem
    - Complementation Theorem
    - Theorem of Total Probability
    - Bayes Theorem
- Random Variables
  - Discrete Random Variables
    - Univariate Case
      - Probability Mass Function
      - Cumulative Distribution Function
      - Expected Value
      - Variance and Standard Deviation
      - Moments
    - Bivariate Case
      - Joint Probability Mass Function
      - Joint Cumulative Distribution Function
      - Marginal Probability Distributions
      - Conditional Probability Distribution
      - Independent Random Variables
      - Covariance and Correlation Coefficient
  - Continuous Random Variables
    - Univariate Case
      - Probability Density Function
      - Cumulative Distribution Function
      - Expected Value
      - Variance
      - Moments
    - Bivariate Case
      - Joint Probability Density Function
      - Joint Cumulative Distribution Function
      - Marginal Probability Distributions
      - Conditional Probability Density Function
      - Independent Random Variables
      - Covariance and Correlation Coefficient
- Discrete Distributions
  - Uniform Distribution
  - Binomial Distribution
  - Poisson Distribution
- Continuous Distributions
  - Uniform Distribution
  - Exponential Distribution
  - Normal Distribution
- Distributions Related to the Normal
  - Chi-Square distribution
  - Student's t-distribution
  - Snedecor's F-distribution
  - Properties of the Sample Mean and Variance
Part II Statistics
- Descriptive Statistics
  - Graphical Data Representation
    - Boxplot
    - Histogram
  - Measures of Location
    - Mean
    - Median
    - Mode
    - Quartiles
  - Measures of Spread
    - Interquartile Range
    - Range
    - Variance and Standard Deviation
- Parameter Estimation
  - Point Estimations
  - Confidence Intervals
    - Confidence Intervals for a Mean
      - Two - Sided Confidence Interval for a Mean when the Variance is Known
      - One - Sided Confidence Interval for a Mean when the Variance is Known
      - Two - Sided Confidence Interval for a Mean when the Variance is Unknown
      - One - Sided Confidence Interval for a Mean when the Variance is Unknown
    - Confidence Intervals for a Difference of Two Means
      - Two - Sided Confidence Interval for a Difference of Means when Variances Are Known
      - One - Sided Confidence Interval for a Difference of Means when Variances Are Known
      - Two-Sided Confidence Interval for a Difference of Means when Variances Are Equal but Unknown
      - One-Sided Confidence Interval for a Difference of Means when Variances Are Equal but Unknown
    - Confidence Intervals for a Variance
      - Two - Sided Confidence Interval for a Variance when the Mean is Known
      - One - Sided Confidence Interval for a Variance when the Mean is Known
      - Two - Sided Confidence Interval for a Variance when the Mean is Unknown
      - One - Sided Confidence Interval for a Variance when the Mean is Unknown
    - Confidence Intervals for a Ratio of Variances
      - Two - Sided Confidence Interval for a Ratio of Variances
      - One - Sided Confidence Interval for a Ratio of Variances
    - Confidence Intervals for a Proportion
      - Two-Sided Confidence Interval for a Proportion: Large Sample
      - One-Sided Confidence Interval for a Proportion: Large Sample
      - Determining the Size of the Sample
    - Confidence Intervals for a Difference of Two Proportions
      - Two-Sided Confidence Interval for a Difference of Proportions
      - One-Sided Confidence Interval for a Difference of Proportions
- Hypothesis Testing
  - General Principles
  - Tests for a Mean
    - Two-Tailed Test for a Mean when the Variance Is Known
    - One-Tailed Test for a Mean when the Variance Is Known
    - Two-Tailed Test for a Mean when the Variance Is Unknown
    - One-Tailed Test for a Mean when the Variance Is Unknown
  - Tests for a Difference of Two Means
    - Two-Tailed Test for a Difference of Means when Variances are Known
    - One-Tailed Test for a Difference of Means when Variances are Known
    - Two-Tailed Test for a Difference of Means when Variances Are Equal but Unknown
    - One-Tailed Test for a Difference of Means when Variances Are Equal but Unknown
  - Tests for a Variance
    - Two-Tailed Test for a Variance when the Mean Is Known
    - One-Tailed Test for a Variance when the Mean Is Known
    - Two-Tailed Test for a Variance when the Mean Is Unknown
    - One-Tailed Test for a Variance when the Mean Is Unknown
  - Tests for an Equality of Two Variances
    - Two-Tailed Test for an Equality of Two Variances
    - One-Tailed Test for an Equality of Two Variances
  - Tests for a Proportion
    - Two-Tailed Test for a Proportion: Large Sample
    - One-Tailed Test for a Proportion: Large Sample
  - Tests for a Difference of Two Proportions
    - Two-Tailed Test for a Difference of Proportions: Large Sample
    - One-Tailed Test for a Difference of Proportions: Large Sample
- Linear Regression
  - The Method of Least Squares
  - The Simple Linear Regression Model
  - Estimating Parameters of a Simple Linear Regression Model
    - Estimating the Slope and Y-intercept of a Simple Linear Regression Model
    - Estimating the Variance of the Random Error Components
  - Confidence Interval for the Y-intercept of a Linear Regression
  - Confidence Interval for the Slope of a Linear Regression
  - Testing the Slope for Model Usefulness
  - Estimating the Mean Value of Y for a Given Value of X
  - Predicting One y-Value for a Given Value of x
  - The Coefficient of Determination
- Analysis of Variance (ANOVA)
  - One - Way Analysis of Variance
    - The One - Way Analysis of Variance Technique
    - The Hypothesis Test in One - Way ANOVA
  - Two - Way Analysis of Variance
    - The Two - Way Analysis of Variance Technique
    - The Hypothesis Tests in Two – Way ANOVA