Click on the arrows to open list of subtopics with respective links

• CHAPTER 1: GENERAL CONCEPTS OF PROBABILITY AND STATISTICS

  1. Random Experiments
  2. Sample Space
  3. Random Variable
  4. Probability Mass Function (PMF), Probability Density Function (PDF), and Cumulative Distribution Function (CDF)
  5. Mathematical Expectation, Mean, Median, Mode, and Percentiles
  6. Interactive Plot With Quartiles: Binomial PMF vs Normal PDF
  7. Variance and Standard Deviation
  8. Covariance
  9. Correlation Coefficient
  10. Skewness and Kurtosis
  11. Moments and Moment Generating Functions
• CHAPTER 2: SIMPLE LINEAR REGRESSION

  1. Sample Datasets
  2. Coefficients
  3. R²
  4. Adjusted R²
  5. The F-Statistic
  6. Standard Errors: residuals, slope and intercept
  7. t-Statistics and p-values: slope and intercept
  8. Confidence Intervals: slope and intercept
  9. Regression Line Confidence Limits
  10. Log-Likelihood, AIC and BIC
  11. Skewness, Kurtosis, Jarque-Bera Test Statistic, Omnibus Test Statistic
  12. Durbin-Watson Statistic
  13. Condition Number
• CHAPTER 3: THE NORMAL DISTRIBUTION

  1. Definition, Equation Derivation, and Example
  2. Confidence Intervals
  3. The Gauss Error Function CDF vs ERF
• CHAPTER 4: THE BINOMIAL DISTRIBUTION

  1. A Bernoulli Trial x_i
  2. Binomial Random Variable X
  3. Expected Values
  4. Distribution Equation
  5. Mean
  6. Variance and Std. Deviation
  7. The Sample Proportion and its Variance
  8. The Moment Generating Function (MFG) and its First Four Moments
  9. Kurtosis
  10. Comparison of the Normal and the Binomial Distributions
  11. Example from the Real World
• CHAPTER 5: THE POISSON DISTRIBUTION

  1. Definition and Derivation
  2. Shape of Distribution for Different Lambda Values
  3. Examples and Applications
  4. Chi-Square in Poisson Distribution