PPT-Probability Theory for

Continued Fractions Lisa Lorentzen Norwegian University of Science and Technology Continued fraction Convergence Möbius transformations Convergence Catch L 1986 General convergence. Through this class we will be relying on concepts from probability theory for deriving machine learning algorithms These notes attempt to cover the basics of probability theory at a level appropriate for CS 229 The mathematical theory of probability Hedonism. . Key players and ideas?. B’s Theory of Motivation. W. hat . is it?. Moral Fact. What is it?. Initial . Ideas. Derivation. : How is the value or norm (idea of goodness which will come from it) derived?. tunity to of six a total of the of being a winner of the and "the last of the of other think that on each is essentially what we mean "heads on toss" are event occurred of the have no of the a poker i Jennifer Trueblood, James . Yearsley. , Peter . Kvam. , Jerome . Busemeyer. , and . Zheng. (Joyce) Wang. Supported by NSF . (SES 0818277, 1153846, 1326275) & AFOSR (FA9550-12-1-00397) . Today’s agenda. 3.1 . The Concept of Probability. 3.2 . Sample Spaces and Events. 3.3 . Some Elementary Probability Rules. 3.4 . Conditional Probability and Independence. 3.5 . Bayes’ Theorem. 3-. 2. Probability Concepts. What we learned last class…. We are not good at recognizing/dealing with randomness. Our “random” coin flip results weren’t streaky enough.. If B/G results behave like independent coin flips, we know how many families to EXPECT with 0,1,2,3,4 girls.. Machine Learning. Chapter 1: Introduction. Example. Handwritten Digit Recognition. Polynomial Curve Fitting . Sum-of-Squares Error Function. 0. th. Order Polynomial. 1. st. Order Polynomial. 3. rd. Conditional Probability. Conditional Probability: . A probability where a certain prerequisite condition has already been met.. Conditional Probability Notation. The probability of Event A, given that Event B has already occurred, is expressed as P(A | B).. March 23, 2010. Outline. Intro & Definitions. Why learn about probabilities and risk?. What is learned?. Expected Utility. Prospect Theory. Scalar Utility Theory. Choices, choices, choices.... In the lab, reinforcement is often uniform. Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 2 Title and Outline. 2. 2. Probability. 2-1 Sample Spaces and Events . 2-1.1 Random Experiments. 2-1.2 Sample Spaces . Probability Theory Section Summary Assigning Probabilities Probabilities of Complements and Unions of Events Conditional Probability Independence Random Variables Assigning Probabilities Let S be a sample space of an experiment with a finite number of outcomes. We assign a probability . SYFTET. Göteborgs universitet ska skapa en modern, lättanvänd och . effektiv webbmiljö med fokus på användarnas förväntningar.. 1. ETT UNIVERSITET – EN GEMENSAM WEBB. Innehåll som är intressant för de prioriterade målgrupperna samlas på ett ställe till exempel:. Mixture of Transparencies created by:. Dr. . Eick. and Dr. Russel. Reasoning and Decision Making Under Uncertainty. Quick Review Probability Theory . Bayes’ Theorem and Naïve Bayesian Systems. Bayesian Belief Networks. 4. Interpret probability as a long-run relative frequency. . Dispel . common myths about randomness.. Use . simulation to model chance behavior.. Randomness, Probability, and Simulation. Randomness, Probability, and Simulation.