PPT-Review: Probability

Random variables events Axioms of probability Atomic events Joint and marginal probability distributions Conditional probability distributions Product rule chain rule Independence and conditional independence. Pieter . Abbeel. UC Berkeley EECS. Many slides adapted from . Thrun. , . Burgard. and Fox, Probabilistic Robotics. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . Random variables, events. Axioms of probability. Atomic events. Joint and marginal probability distributions. Conditional probability distributions. Product . rule, chain rule. Independence and conditional independence. B. y. Daniel Christie. Probability. In a class of four brunettes, two blondes, and two people with black hair, what is the probability that any given person would be blonde?. 1/4. Venn Diagrams. Tree Diagrams. Experimental probability. : . Probability based on a collection of data.. Will have a table of results or data from the experiment(s)!. What is the difference between . theoretical probability. and . Random Variables. Definition:. A rule that assigns one (and only one) numerical value to each simple event of an experiment; or. A function that assigns numerical values to the possible outcomes of an experiment.. Probability Terminology. Classical Interpretation. : Notion of probability based on equal likelihood of individual possibilities (coin toss has 1/2 chance of Heads, card draw has 4/52 chance of an Ace). Origins in games of chance.. 4. Introduction. (slide 1 of 3). A key . aspect of solving real business problems is dealing appropriately with uncertainty.. This involves recognizing explicitly that uncertainty exists and using quantitative methods to model uncertainty.. 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.. 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 . 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 . A value between zero and one that describe the relative possibility(change or likelihood) an event occurs.. The MEF announces that in 2012 the change Cambodia economic growth rate is equal to 7% is 80%.. 4. Compute the number of combinations of . n. individuals taken . k. at a time.. Use . combinations to calculate probabilities.. Use . the multiplication counting principle and combinations to calculate probabilities.. 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.