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.: . http://mikeess-trip.blogspot.com/2011/06/gambling.html. 1. Uses of Probability. Gambling. Business. Product preferences of consumers. Rate of returns on investments. Engineering. Defective parts. Physical Sciences. 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. Mat 271E. Yard. Doç. Dr. Tarkan Erdik. Probability Distributions. Uniform and Normal Distributions- Week 7. 1. Probability Distributions. 2. It has been observed that . certain functions . F(x). and . Coins game. Toss 3 coins. You win if . at least two . come out heads. S. = { . HHH. , . HHT. , . HTH. , . HTT. , . T. HH. , . T. HT. , . T. TH. , . T. TT. }. equally likely outcomes. W. = { . HHH. Section 5.1. An event is the set of possible outcomes. Probability is between 0 and 1. The event A has a complement, the event not A. Together these two probabilities sum 1.. . ex. At least one and none are complements. calculus. 1 ≥ . Pr. (h) ≥ 0. If e deductively implies h, then Pr(h|e) = 1. .. (disjunction rule) If h and g are mutually exclusive, then . Pr. (h or g) = . Pr. (h) . Pr. (g). (disjunction rule) If h and g are . 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.. 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).. Slide . 2. Probability - Terminology. Events are the . number. of possible outcome of a phenomenon such as the roll of a die or a fillip of a coin.. “trials” are a coin flip or die roll. Slide . Probability and Probability Distribution Dr Manoj Kumar Bhambu GCCBA-42, Chandigarh M- +91-988-823-7733 mkbhambu@hotmail.com Probability and Probability Distribution: Definitions- Probability Rules –Application of Probability calculus. 1 ≥ . Pr. (h) ≥ 0. If e deductively implies h, then Pr(h|e) = 1. .. (disjunction rule) If h and g are mutually exclusive, then . Pr. (h or g) = . Pr. (h) + . Pr. (g). (disjunction rule) If h and g are . A jar contains 10 purple marbles and 2 red marbles. If two marbles are chosen at random with no replacement, what is the probability that 2 purple marbles are chosen? . A bag contains 6 cherry, 8 strawberry, and 9 grape-flavored candies. What is the probability of selecting a cherry or a grape-flavored candy?. 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.