Probability and Statistics form the foundation of data analysis and decision-making in nearly every modern discipline — from computer science and machine learning to finance and healthcare. This introduction covers the core principles, techniques, and applications of both fields. Whether you're analyzing trends or making predictions, understanding probability and statistics is essential.
1. Counting Principles
Learn the fundamental rules of counting: addition and multiplication principles, permutations (with and without repetition), combinations, and circular permutations, which are foundational to probability calculations.
2. Probability Axioms & Basics
Understand the axioms of probability including non-negativity, total probability, and additivity. These rules help in defining valid probability measures over sample spaces.
3. Sample Space and Events
Define sample spaces for different experiments and classify events as simple, compound, certain, or impossible. Apply set operations like union, intersection, and complement.
4. Independent & Mutually Exclusive Events
Learn how to determine if events are independent or mutually exclusive and how these affect combined probabilities.
5. Joint, Marginal & Conditional Probability
Explore how to calculate joint, marginal, and conditional probabilities and understand their roles in real-world data scenarios.
6. Bayes’ Theorem
Learn how to update probabilities based on new information using Bayes’ Theorem. Commonly used in machine learning, medicine, and spam filtering.
7. Random Variables and Distributions
Understand discrete and continuous random variables, PMFs, PDFs, and commonly used distributions like Binomial, Poisson, Normal, and Exponential.
8. Central Limit Theorem (CLT)
Discover how the Central Limit Theorem enables approximation of distributions and forms the backbone of many statistical methods.
9. Confidence Intervals & Hypothesis Testing
Learn how to draw inferences from data by constructing confidence intervals and performing hypothesis tests like z-tests, t-tests, and chi-squared tests.