Chapter 1: Introduction to Statistics and Probability
- Lesson 1: What is Statistics?
- Lesson 2: What is Probability?
- Lesson 3: Importance and Applications
- Lesson 4: Types of Data (Qualitative vs Quantitative)
- Lesson 5: Overview of the Course
Chapter 2: Data Collection and Sampling
- Lesson 1: Population vs Sample
- Lesson 2: Sampling Methods (Random, Systematic, etc)
- Lesson 3: Designing Surveys and Experiments
- Lesson 4: Sources of Bias
- Lesson 5: Ethical Considerations in Data Collection
Chapter 3: Descriptive Statistics
- Lesson 1: Measures of Central Tendency (Mean, Median, Mode)
- Lesson 2: Measures of Spread (Range, Variance, Standard Deviation)
- Lesson 3: Frequency Distributions and Histograms
- Lesson 4: Percentiles and Quartiles
- Lesson 5: Box-and-Whisker Plots
- Lesson 6: Skewness and Kurtosis
Chapter 4: Data Visualization
- Lesson 1: Bar Charts and Pie Charts
- Lesson 2: Line Graphs and Scatter Plots
- Lesson 3: Stem-and-Leaf Plots
- Lesson 4: Heatmaps
- Lesson 5: Choosing the Right Visualization
Chapter 5: Probability Basics
- Lesson 1: Definitions of Probability
- Lesson 2: Probability Rules (Addition, Multiplication)
- Lesson 3: Conditional Probability
- Lesson 4: Independent vs Dependent Events
- Lesson 5: Complementary and Mutually Exclusive Events
Chapter 6: Random Variables and Probability Distributions
- Lesson 1: What are Random Variables?
- Lesson 2: Discrete vs Continuous Random Variables
- Lesson 3: Probability Distribution Functions (PDFs)
- Lesson 4: Cumulative Distribution Functions (CDFs)
- Lesson 5: Expected Value and Variance
Chapter 7: Basic Probability Models
- Lesson 1: Uniform Distribution
- Lesson 2: Binomial Distribution
- Lesson 3: Poisson Distribution
- Lesson 4: Geometric Distribution
- Lesson 5: Hypergeometric Distribution
Chapter 8: Introduction to Hypothesis Testing
- Lesson 1: Null and Alternative Hypotheses
- Lesson 2: Errors in Hypothesis Testing (Type I & Type II)
- Lesson 3: P-value and Significance Level
- Lesson 4: One-Tailed vs Two-Tailed Tests
- Lesson 5: Overview of the Testing Process
Chapter 9: Correlation and Linear Regression
- Lesson 1: Understanding Correlation
- Lesson 2: Scatter Plots and Correlation Coefficient
- Lesson 3: Basics of Linear Regression
- Lesson 4: Interpreting Slope and Intercept
- Lesson 5: Goodness of Fit (R²)
Chapter 10: Normal Distribution
- Lesson 1: Properties of the Normal Curve
- Lesson 2: Z-Scores and Standardization
- Lesson 3: Empirical Rule (68-95-99.7)
- Lesson 4: Applications of Normal Distribution
- Lesson 5: Central Limit Theorem
Chapter 11: Inferential Statistics
- Lesson 1: Point Estimation vs Interval Estimation
- Lesson 2: Confidence Intervals
- Lesson 3: Margin of Error
- Lesson 4: Sampling Distributions
- Lesson 5: Applications in Real-World Scenarios
Chapter 12: Introduction to Statistical Software
- Lesson 1: Overview of Tools (Excel, R, Python, SPSS)
- Lesson 2: Data Entry and Manipulation
- Lesson 3: Basic Analysis with Software
- Lesson 4: Generating Visualizations
- Lesson 5: Exporting and Reporting Results
Chapter 13: Chi-Square Tests
- Lesson 1: Introduction to Chi-Square Tests
- Lesson 2: Goodness-of-Fit Test
- Lesson 3: Test for Independence
- Lesson 4: Applications and Interpretations
- Lesson 5: Assumptions and Limitations
Chapter 14: Non-Parametric Tests
- Lesson 1: Introduction to Non-Parametric Methods
- Lesson 2: Wilcoxon Signed-Rank Test
- Lesson 3: Mann-Whitney U Test
- Lesson 4: Kruskal-Wallis Test
- Lesson 5: Applications of Non-Parametric Tests
Chapter 15: Advanced Data Visualization
- Lesson 1: 1Interactive Dashboards
- Lesson 2: 3D Visualizations
- Lesson 3: Custom Infographics
- Lesson 4: Advanced Tools (Tableau, Power BI)
- Lesson 5: Storytelling with Data
Chapter 16: Basics of Experimental Design
- Lesson 1: Principles of Experimental Design
- Lesson 2: Randomized Control Trials
- Lesson 3: Factorial Design
- Lesson 4: Block Design
- Lesson 5: Applications in Practice
Chapter 1: Advanced Probability Concepts
- Lesson 1: Bayes’ Theorem
- Lesson 2: Law of Total Probability
- Lesson 3: Joint, Marginal, and Conditional Distributions
- Lesson 4: Independence and Dependence in Depth
- Lesson 5: Advanced Probability Rules
Chapter 2: Advanced Random Variables and Distributions
- Lesson 1: Multivariate Random Variables
- Lesson 2: Transformations of Variables
- Lesson 3: Exponential and Gamma Distributions
- Lesson 4: Weibull and Beta Distributions
- Lesson 5: Extreme Value Theory
Chapter 3: Bayesian Statistics
- Lesson 1: Bayesian Inference Basics
- Lesson 2: Prior, Likelihood, Posterior, and Evidence
- Lesson 3: Applications of Bayes’ Rule
- Lesson 4: Bayesian vs Frequentist Approaches
- Lesson 5: Markov Chain Monte Carlo (MCMC)
Chapter 4: Statistical Inference Techniques
- Lesson 1: Advanced Hypothesis Testing
- Lesson 2: Power Analysis
- Lesson 3: Non-Parametric Tests
- Lesson 4: Bootstrapping and Resampling
- Lesson 5: Permutation Tests
Chapter 5: Multivariate Statistics
- Lesson 1: Multivariate Normal Distribution
- Lesson 2: Principal Component Analysis (PCA)
- Lesson 3: Factor Analysis
- Lesson 4: Cluster Analysis
- Lesson 5: Canonical Correlation Analysis
Chapter 6: Advanced Regression Models
- Lesson 1: Multiple Linear Regression
- Lesson 2: Polynomial Regression
- Lesson 3: Logistic Regression
- Lesson 4: Ridge and Lasso Regression
- Lesson 5: Regression Diagnostics
Chapter 7: Time Series Analysis
- Lesson 1: Components of Time Series
- Lesson 2: ARIMA Models
- Lesson 3: Seasonal Decomposition
- Lesson 4: Forecasting Techniques
- Lesson 5: Applications in Finance and Economics
Chapter 8: Survival Analysis
- Lesson 1: Kaplan-Meier Curves
- Lesson 2: Hazard Functions
- Lesson 3: Cox Proportional Hazards Model
- Lesson 4: Right-Censored Data
- Lesson 4: Applications in Medicine
Chapter 9: Bayesian Hierarchical Models
- Lesson 1: Hierarchical Structures in Data
- Lesson 2: Multilevel Modeling
- Lesson 3: Bayesian Priors in Hierarchical Models
- Lesson 4: Case Studies
- Lesson 5: Advanced Applications
Chapter 10: Markov Processes
- Lesson 1: Introduction to Markov Chains
- Lesson 2: Transition Matrices
- Lesson 3: Steady-State Probabilities
- Lesson 4: Applications of Markov Processes
- Lesson 5: Hidden Markov Models
Chapter 11: Spatial Statistics
- Lesson 1: Basics of Spatial Data
- Lesson 2: Point Pattern Analysis
- Lesson 3: Spatial Autocorrelation
- Lesson 4: Geostatistics (Kriging, Variograms)
- Lesson 5: Applications in Geography and Environmental Science
Chapter 12: Advanced Statistical Computing
- Lesson 1: Simulation Techniques
- Lesson 2: Monte Carlo Methods
- Lesson 3: Numerical Optimization
- Lesson 4: Parallel Computing in Statistics
Chapter 13: Experimental Design and ANOVA
- Lesson 1: Advanced Principles of Experimental Design
- Lesson 2: ANOVA (One-Way, Two-Way, MANOVA)
- Lesson 3: Randomized Block Design
- Lesson 4: Repeated Measures
- Lesson 5: Applications in Real Experiments
Chapter 14: Advanced Data Ethics
- Lesson 1: Ethical Issues in Data Science
- Lesson 2: Privacy and Security in Statistical Analysis
- Lesson 3: Bias and Fairness in Algorithms
- Lesson 4: Responsible Data Sharing
- Lesson 5: Case Studies in Data Ethics
Chapter 15: Emerging Topics in Statistics
- Lesson 1: Functional Data Analysis
- Lesson 2: Causal Inference
- Lesson 3: Statistical Genetics
- Lesson 4: Advanced Optimization Techniques
- Lesson 5: Applications in AI and Robotics
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