PPT-Review of Probability

Jake Blanchard Spring 2010 Uncertainty Analysis for Engineers 1 Introduction Interpretations of Probability Classical If an event can occur in N equally likely and different ways and if n of these have an attribute A then the probability of the occurrence of A denoted PrA is defined as nN. 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 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.: . Understanding the meaning of the terminology we use.. Quick calculations that indicate understanding of the basis of methods.. Many of the possible questions are already sprinkled in the lecture slides.. T.Jagannadha. . Swamy. Dept of . ECE,Griet. Random Variable. A random variable . x. takes on a defined set of values with different probabilities.. For example, if you roll a die, the outcome is random (not fixed) and there are 6 possible outcomes, each of which occur with probability one-sixth. . Random variables, events. Axioms of probability. Atomic events. Joint and marginal probability distributions. Conditional probability distributions. Product . rule, chain rule. Independence and conditional independence. . Jim-Bob comes home from work and finds Slobber lying on the porch sick from eating half of the items in the basket. He rushes him to the vet. The vet gives the dog medicine with a dosage of 1 . tsp. . Chapter 1 - Overview and Descriptive Statistics. . Chapter 2 - Probability. . Chapter 3 - Discrete Random Variables and Probability Distributions. Chapter 4 - Continuous Random Variables and Probability Distributions. 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. 1. Suppose that . A. and . B. are independent events with . P. (. A. ) = 0.2 and . P. (. B. ) = 0.4. . is. :. a) 0.08. b) 0.12. c) 0.44. . d. ) 0.52. e) 0.60.. Notes on . Ch. 15 part . 1. We will review conditional probability, then we will learn how to test for independence, and calculate probabilities for events that draw without replacement.. Agenda. Objective. - Modified Jeopardy. Name. that Chi-square. Analyst Choice. Pesky Assumptions. Interpretation Mania. Regression Junction. 100. 100. 100. 100. 100. 200. 200. 200. 200. 200. 300. 300. 300. 300. 300. 400. 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?. Jiaping. Wang. Department of Mathematical Science . 02/18/2013, Monday. Outline. . Sample Space and Events. . Definition of Probability. Counting Rules. Conditional Probability and Independence. 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.