0
Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

# Cs221 probability theory

258

Published on

Published in: Technology, Education
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• Be the first to comment

• Be the first to like this

Views
Total Views
258
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
17
0
Likes
0
Embeds 0
No embeds

No notes for slide
• 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&#x2022; Axioms of Probability&#x2022; Product and chain rules&#x2022; Bayes Theorem&#x2022; Random variables&#x2022; PDFs and CDFs&#x2022; Expected value and variance
• 3. Introduction&#x2022; Sample space - set of all possible outcomes of a random experiment &#x2013; Dice roll: {1, 2, 3, 4, 5, 6} &#x2013; Coin toss: {Tails, Heads}&#x2022; Event space - subsets of elements in a sample space &#x2013; Dice roll: {1, 2, 3} or {2, 4, 6} &#x2013; Coin toss: {Tails}
• 4. Introduction
• 5. Set operations
• 6. Conditional Probability A B
• 7. Conditional Probability &#x3A9; 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?