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ECON 2B03 (10)
Chapter 4

Lecture #8- Chapter 4 and 5 (Probability).doc

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Jeff Racine

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Lecture # 7- Beginning of Chapters 4 and 5 Basic Probability Concepts • We now lay the foundation for the field of statistical inference by studying the theory of probability • Statistical Inference: A set of techniques that allows us to turn sample evidence into conclusions about statistical populations of interest • Theory of Probability: Calculus of the likelihood of specific occurrences -Gives rise to entire field of inferential statistics -Points to likely point us towards a likely truth even though we cant know the truth with certainty. (Beginning of Lecture #8) • Experiment: Any repeatable process from which an outcome measurement, or result is obtained (It is something we can repeat). • Random Experiment o Definition: An experiment whose outcome cannot be predicted with certainty o Any activity that results in one and only one of several clearly definied possible outcomes (ie: a number), but that does not allow us to tell in advance which of these will prevail in any particular instance • Sample Space o Definition: A listing of all the basic outcomes of a random experiment, also known sometimes as the (Outcome Space, Probability Space) o Examples: -Tossing a single coin one -Rolling a single die once -Drawing a single card once • Random Event o Definition: Subset of the sample space • Simple Event o Definition: An single basic outcome from a random experiment o Univariable, Bivariate (2 variables), multivariate (more than 2 variables) • Composite Event o Any combination of two or more basic outcomes Examples: Ask two people if interest rates are going up They must awnser “yes” or “no” Simple events: a =(Y, Y), a =(Y, N), a =(N, Y), a4=(N,N) 1 2 3 Sample Space: U= a1,a2,a3,a4 Could definie more interesting composite event such as event A “at least on person said yes”, in which the event A1= [a1,a2,a3] while A2=[a2] How Random Events Relate • Mutually Exclusive Events o Definition: Random Events that have no outcomes in common o Often also called disjoint or incompatible events • Collectively Exhaustive Events o Definition: Random Events that contain all basic outcomes in the sample space o When the appropriate random experiment is collected, one of these events is bound to occur Ie: ask 2 ppl if the interest is going up, if one person says yes than it is successful (a1, a2, a3) and the other didn’t?? • Complementary Events o Two random events for which all basic outcomes not contained in one event are contained in the other event o Such events are usually both mutually exhaustive at the same time • Unisons of Events (logical operator U –symbol [or]) o All basic outcomes contained in one or the other event • Intersections of Events (logical operator upsidedown U [and]) o All basic outcomes contained in one and the other event *On the midterm he will give examples of outcomes and will ask if they are mutually exclusive or collective exhaustive* Probability Concepts • Objective Probability:
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