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Unformatted text preview: PROBABILITY THEORY Dr. V.R. Bencivenga Economic Statistics Economics 329 PROBABILITY THEORY — PART 1 Outline Why do we need probability theory? Concepts of probability Sets and events Set operations Probability postulates Objectives: How to define and work with random events. Lay out the logical structure underlying the rules of probability. 2 PROBABILITY THEORY WHY DO WE NEED PROBABILITY THEORY? 3 PROBABILITY THEORY We need probability for games of chance (backgammon, poker, bridge) Also placing bets (commodities) modeling financial portfolios … 4 PROBABILITY THEORY What do these situations have in comm on? Outcomes … dots on dice, cards played prices stock prices, bond yields, exchange rates … arise from a random proces s … tossing dice, shuffling cards demand and supply financial markets, foreign exchange markets, interest rates, … We need probability to compute our best “action” or “strategy.” 5 PROBABILITY THEORY Now consider the following questions: A bank has been accused of discriminating against minority applicants for mortgages. The prosecutor presents evidence for 12 minority applicants and 15 nonminority applicants (number approved in each group). Did the bank discriminate? Microfinance (small loans given to groups of poor borrowers) has been touted as an important financial innovation. An economist wants to study whether microfinance improves living standards (average consumption, variability of consumption). Her data cover several hundred families in 5 shantytowns in a developing country, 3 where an MFI went in and offered loans, 2 with no MFI. Does microfinance improve lives? Is the fami ly’s consumption higher and/or “smoother?” 6 PROBABILITY THEORY These data also were generated by random processes: An applicant with certain characteristics (minority/nonminority, credit score, income, etc.) applies for a mortgage. Both applicant characteristics and random factors influence whether it ’s approved. A poor family (with or without access to a microfinance loan) works and earns income, and then consumes, i.e., the family buys food, clothing, shelter, etc. Access to a loan and other characteristics influence the level and “smoothness” of the family’s consumption, but so do random factors such as weather (which affects prices), interest rates, the supply of credit, etc. 7 PROBABILITY THEORY We are studying physical or social or economic process es (DGP’s) we can measure, where (1) there is regularity in the process The set of possible outcomes is known, and although we can’t observe it, the distribution of probability over possible outcomes is stable....
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This note was uploaded on 02/26/2012 for the course ECONOMICS 329 taught by Professor Bencivenga during the Spring '12 term at University of Texas.
 Spring '12
 BENCIVENGA
 Economics

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