Probability Theory
Welcome to the Probability Theory course! 🎲🧮 This foundational subject explores the mathematical principles behind uncertainty and randomness, essential for fields like statistics, machine learning, and data science. Here's what you'll learn:
📚 Core Topics
- Basic Concepts: Probability axioms, sample spaces, events, and random variables.
- Distributions: Discrete (e.g., Bernoulli, Poisson) vs. continuous (e.g., Normal, Exponential).
- Conditional Probability & Bayes' Theorem: Understanding dependencies and updating beliefs with evidence.
- Random Processes: Markov chains, stochastic processes, and their applications.
- Expectation & Variance: Quantifying central tendency and spread of random phenomena.
🌐 Applications
- Data Science: Predictive modeling and risk assessment.
- Engineering: Reliability analysis and quality control.
- Finance: Portfolio optimization and market forecasting.
- Computer Science: Algorithms for probabilistic reasoning and AI.
For deeper exploration, check out our Statistics Course to see how probability and statistics intertwine! 📈
This course also covers law of large numbers and central limit theorem, which are pivotal for statistical inference. Don’t forget to explore our Machine Learning Path to apply these concepts practically! 🚀