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Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
Cs221 probability theory
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Cs221 probability theory

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  • A in unobserved, but B is observed
  • A in unobserved, but B is observed
  • F(x) is monotonically non-decreasing
  • PDF is also called probability mass function when applied to discrete random variables
  • PDF is also called probability mass function when applied to discrete random variables
  • PDF is also called probability mass function when applied to discrete random variables
  • PDF is also called probability mass function when applied to discrete random variables
  • PDF is also called probability mass function when applied to discrete random variables
  • PDF is also called probability mass function when applied to discrete random variables
  • PDF is also called probability mass function when applied to discrete random variables
  • PDF is also called probability mass function when applied to discrete random variables
  • PDF is also called probability mass function when applied to discrete random variables
  • Transcript

    • 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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