Unit 1266: Probability and Statistics Fundamentals

1. Introduction to Probability

• Definition of Probability
• Sample Spaces and Events
  • Simple Events
  • Compound Events
• Calculating Probabilities
  • Classical Probability
  • Empirical Probability
  • Subjective Probability

2. Probability Rules

• Addition Rule
  • For Mutually Exclusive Events
  • For Non-Mutually Exclusive Events
• Multiplication Rule
  • Independent Events
  • Dependent Events
• Conditional Probability
  • Definition and Formula
  • Applications
• Complement Rule

3. Probability Distributions

• Discrete Probability Distributions
  • Definition and Examples (e.g., Binomial Distribution, Poisson Distribution)
  • Probability Mass Function (PMF)
• Continuous Probability Distributions
  • Definition and Examples (e.g., Normal Distribution, Exponential Distribution)
  • Probability Density Function (PDF)
• Calculating Probabilities Using Distribution Functions

4. Descriptive Statistics

• Measures of Central Tendency
  • Mean
  • Median
  • Mode
• Measures of Dispersion
  • Range
  • Variance
  • Standard Deviation
• Data Visualization Techniques (Optional)
  • Histograms
  • Box Plots

5. Inferential Statistics

• Principles of Inferential Statistics
• Hypothesis Testing
  • Null and Alternative Hypotheses
  • Types of Errors (Type I and II)
  • Test Statistics and P-values
  • Common Tests (z-test, t-test)
• Confidence Intervals
  • Definition and Interpretation
  • Calculating Confidence Intervals for Means and Proportions
• Using Sample Data to Infer Population Parameters

6. Correlation and Regression

• Correlation Analysis
  • Definition and Interpretation of Correlation Coefficient
  • Types: Positive, Negative, and No Correlation
• Regression Analysis
  • Simple Linear Regression
  • Fitting Regression Models
  • Interpreting Regression Coefficients
  • Assessing Model Fit (R-squared)

7. Probability and Statistics in Real Life

• Application of Probability in Decision Making
• Analyzing Data Trends
• Making Predictions Based on Statistical Models
• Understanding Randomness and Variability in Real World
• Case Studies and Examples