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- 1. Probability Theory Review CS221: Introduction to Artificial Intelligence Naran Bayanbat 10/14/2011Slides used material from CME106 course reader and CS229 handouts
- 2. Topics• Axioms of Probability• Product and chain rules• Bayes Theorem• Random variables• PDFs and CDFs• Expected value and variance
- 3. Introduction• Sample space - set of all possible outcomes of a random experiment – Dice roll: {1, 2, 3, 4, 5, 6} – Coin toss: {Tails, Heads}• Event space - subsets of elements in a sample space – Dice roll: {1, 2, 3} or {2, 4, 6} – Coin toss: {Tails}
- 4. Introduction
- 5. Set operations
- 6. Conditional Probability A B
- 7. Conditional Probability Ω A B
- 8. Conditional Probability
- 9. Conditional Probability
- 10. Conditional Probability
- 11. Conditional ProbabilityP(A, B) 0.005P(B) 0.02P(A|B) 0.25
- 12. Bayes Theorem
- 13. Bayes Theorem PosteriorProbability Likelihood Prior Normalizing Probability Constant
- 14. Bayes Theorem
- 15. Random Variables Do ya feel lucky, punk?
- 16. Cumulative Distribution Functions
- 17. Probability Density Functions
- 18. Probability Density Functions
- 19. Probability Density Functions
- 20. Probability Density Functions f(X) X
- 21. Probability Density Functions f(X) X
- 22. Probability Density Functions f(x) x F(x) 1 x
- 23. Probability Density Functions f(x) x F(x) 1 x
- 24. Expectation
- 25. Expectation
- 26. Variance
- 27. Gaussian Distributions
- 28. Questions?

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