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Basic probability & statistics

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Introduction to Probability and Statistic

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Basic probability & statistics

  1. 1. Basic Probability and Statistic Editor: Nguyen Duc Minh Khoi Email: ducminhkhoi@gmail.com Website: https://nguyenducminhkhoi.blogspot.com
  2. 2. Probability: The basics
  3. 3. Probability: The basics (cont.) • Conditional Probability • Independence
  4. 4. Probability: The basics (cont.) • Rule of total Probability: • Bayes Rule: • Chain rule       ii BAPBPAp |   )( )|()( | yP xyPxP yxP 
  5. 5. Probability: Random Variable (rv) – PMF vs. PDF • Discrete RV • Continuous RV
  6. 6. Probability: Random Variable (rv) - Cumulative Density Functions (CDF)
  7. 7. Probability: Expectations
  8. 8. Probability: Expectations (cont.) • Conditional expectation
  9. 9. Probability: Expectations (cont.) • Other important Values • Example:
  10. 10. Probability: Important discrete rv
  11. 11. Probability: Important continuous rv
  12. 12. Probability: Multiple variables
  13. 13. Probability: Multiple variables (Covariance & Correlation)
  14. 14. Law of large number & Central Limit Theorem
  15. 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. 16. Classical Inference: Maximum Likelihood Estimator (MLE) Step: 1. Log; 2. derive; 3. solve for 𝜃
  17. 17. Classical Inference: Other methods • Linear Regression
  18. 18. Bayesian Inference:
  19. 19. Bayesian Inference (cont.)
  20. 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.

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