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eco331-01-IntroHandout

# eco331-01-IntroHandout - Introduction Probability Random...

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Introduction Probability Random Variables Expectation Joint Distributions Summary Infinite State Space Eco331: Introduction Marciano Siniscalchi September 23, 2009

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Introduction Probability Random Variables Expectation Joint Distributions Summary Infinite State Space Logistics and General Info Welcome to Economics of Risk and Uncertainty , Fall ’09 Edition! Logistics Office hours Monday, 4pm–5pm, Jacobs Center 3223. TA section led by Ahmad Peivandi. Friday, same place/time. Blackboard for lecture notes, homeworks, notices... Grading etc. Homework 20%, Midterm 30%, Final 50%. No late homeworks/make-up midterm! Magic formula. Readings Lecture notes. Optional: Eeckhoudt, Gollier and Schlesinger. WARNING: this course is very math-intensive!
Introduction Probability Random Variables Expectation Joint Distributions Summary Infinite State Space Overview Three main topics: 1 Subjective Probability and Bayesian Inference (basics) 2 Static (one-period) choice 3 Information and Dynamic Choice Focus on applications , but rigorous formal analysis. Examples: Portfolio Choice Insurance Pricing under Uncertainty Consumption-Savings Problems Dynamic Programming

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Introduction Probability Random Variables Expectation Joint Distributions Summary Infinite State Space A Crash Course in “serious” Probability Theory You have seen probability, random variables, expectation... ...but perhaps not quite the “right” way (for Eco331)! Formal treatment scary at first, but simplifies things!!! Overview: Set theory, states, events Probability as a function Random variables as functions Expectation of Random Variables Conditional Probability and Independence Mostly “finite setting” but discuss general case, too. Throughout this course, use finite or continuous setting depending on which is easier!
Introduction Probability Random Variables Expectation Joint Distributions Summary Infinite State Space Set Theory: states Consider an experiment : e.g. die roll . Want to represent facts that are uncertain prior to rolling the die : Will the outcome be even? Will it be exactly 3? Will it be divisible by 3? Some “facts” pin down the realization uniquely: call them states . Definition A state (of nature) or elementary event is an exhaustive description of exactly one possible outcome. The state space is the collection of all states of nature. Also called sample space . State space for die roll: S = n 1 , 2 , 3 , 4 , 5 , 6 o . A state: s = 3 , i.e. “the outcome is exactly 3.”

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Introduction Probability Random Variables Expectation Joint Distributions Summary Infinite State Space Set Theory: events Again consider die roll . How about “the outcome is even”? Not a state, but corresponds to E = n 2 , 4 , 6 o . Definition An event in a state space S is a subset E of S , written E S . The set of all events, or power set of S , is denoted by P ( S ).
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eco331-01-IntroHandout - Introduction Probability Random...

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