Welcome to your complete Statistics learning roadmap. This page shows the full journey — from the very basics of describing data all the way to advanced limit theorems. Use it as a checklist while you study.
How to Use This Syllabus
Start from Section 1 and move in order. Master each topic with examples and practice before going further. This sequence builds a strong foundation step by step.
1. Descriptive Statistics
Foundation
Learn how to summarise and describe data clearly.
Measures of Central Tendency
- Arithmetic Mean
- Median
- Mode
Measures of Dispersion
- Range
- Variance
- Standard Deviation
Relationship Measures
- Covariance
- Correlation
- Properties of Covariance and Correlation
2. Random Variables
Core
Understand the numerical outcomes of random experiments.
- Discrete Random Variables
- Continuous Random Variables
- Probability Mass Function (PMF)
- Probability Density Function (PDF)
- Cumulative Distribution Function (CDF)
3. Probability Distributions
Important
Discrete Distributions
- Bernoulli Distribution
- Binomial Distribution
- Poisson Distribution
Continuous Distributions
- Uniform Distribution
- Exponential Distribution
- Normal Distribution
- Standard Normal Distribution
4. Joint Probability Distributions
Advanced Basics
Study two or more random variables together.
- Joint Distributions
- Marginal Distributions
- Conditional Distributions
- Independence of Random Variables
5. Mathematical Expectation
Key Theory
Learn the long-run average behaviour of random variables.
- Expected Value of a Random Variable
- Properties of Expectation
- Variance of a Random Variable
- Properties of Variance
- Conditional Expectation
- Conditional Variance
6. Limit Theorems
Advanced
Powerful results that help us approximate distributions for large samples.
- Central Limit Theorem (CLT)
- Applications of the Central Limit Theorem
Suggested Study Order
- Finish Descriptive Statistics thoroughly
- Master Random Variables + PMF / PDF / CDF
- Learn the main Discrete & Continuous distributions
- Move to Joint Distributions and Independence
- Study Expectation and Variance in depth
- Finally understand the Central Limit Theorem and its uses
Ready to start? The next lesson will begin with Descriptive Statistics – Measures of Central Tendency.
