Basic probability & statistics
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This document provides an overview of basic probability and statistics concepts. It discusses topics like probability, random variables, expectations, important distributions, multiple variables, law of large numbers, central limit theorem, classical inference including maximum likelihood estimation, Bayesian inference, and references several textbooks and online courses for further information. The document is authored by Nguyen Duc Minh Khoi and provides his contact information.
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Basic probability & statistics
- 1. Basic Probability and Statistic Editor: Nguyen Duc Minh Khoi Email: ducminhkhoi@gmail.com Website: https://nguyenducminhkhoi.blogspot.com
- 3. Probability: The basics (cont.) • Conditional Probability • Independence
- 4. Probability: The basics (cont.) • Rule of total Probability: • Bayes Rule: • Chain rule ii BAPBPAp | )( )|()( | yP xyPxP yxP
- 5. Probability: Random Variable (rv) – PMF vs. PDF • Discrete RV • Continuous RV
- 6. Probability: Random Variable (rv) - Cumulative Density Functions (CDF)
- 8. Probability: Expectations (cont.) • Conditional expectation
- 9. Probability: Expectations (cont.) • Other important Values • Example:
- 13. Probability: Multiple variables (Covariance & Correlation)
- 14. Law of large number & Central Limit Theorem
- 15. Statistics • Give data, how to find the model (pattern) of this data. • 2 school of thoughts: • 𝜃in Bayesian is a rv (have prior p(𝜃)); 𝜃 in Classical is unknown constant.
- 16. Classical Inference: Maximum Likelihood Estimator (MLE) Step: 1. Log; 2. derive; 3. solve for 𝜃
- 17. Classical Inference: Other methods • Linear Regression
- 20. References • http://www.stanford.edu/class/cme308/OldWebsit e/notes/chap2.pdf • http://ocw.mit.edu/courses/electrical-engineering- and-computer-science/6-041sc-probabilistic- systems-analysis-and-applied-probability-fall- 2013/resource-index/ • Bertsekas, Dimitri P. Introduction to Probability: Dimitri P. Bertsekas and John N. Tsitsiklis. Athena scientific, 2002.