,院究所膏装南鱼王季大門厦鼻 NG YA Foundation of Probability Theory Professor Yongmiao Hong Cornell University May22,2019
Foundation of Probability Theory Professor Yongmiao Hong Cornell University May 22, 2019
CONTENTS 2.1 Random Experiments 2.2 Basic Concepts of Probability 2.3 Review of Set Theory 2.4 Fundamental Probability Laws 2.5 Methods of Counting 2.6 Conditional Probability 2.7 Bayes'Theorem 2.8 Independence 2.9 Conclusion Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 2/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 2/248 2.1 Random Experiments 2.2 Basic Concepts of Probability 2.3 Review of Set Theory 2.4 Fundamental Probability Laws 2.5 Methods of Counting 2.6 Conditional Probability 2.7 Bayes' Theorem 2.8 Independence 2.9 Conclusion CONTENTS
Foundation of Probability Theory Random Experiments Random Experiments Recall fundamental axioms of econometrics: Axiom A:An economic system can be viewed as a random experiment governed by some probability law. Axiom B:Any economic phenomenon (often in form of data)can be viewed as an out-come of this random experiment.The random experiment is called a "data generating process". Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 3/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 3/248 Recall fundamental axioms of econometrics: ● Axiom A: An economic system can be viewed as a random experiment governed by some probability law. ● Axiom B: Any economic phenomenon (often in form of data) can be viewed as an out-come of this random experiment. The random experiment is called a “data generating process". Random Experiments Foundation of Probability Theory Random Experiments
Foundation of Probability Theory Random Experiments Random Experiments Question:How to characterize a random system or stochastic process? Definition 1.Random Experiment A random experiment is a mechanism which has at least two possible outcomes. When a random experiment is performed,one and only one outcome will occur,but which outcome to occur is unknown in advance. Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 4/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 4/248 Random Experiments Random Experiments Question: How to characterize a random system or stochastic process? Definition 1. [ Random Experiment ] A random experiment is a mechanism which has at least two possible outcomes. When a random experiment is performed, one and only one outcome will occur, but which outcome to occur is unknown in advance. Foundation of Probability Theory
Foundation of Probability Theory Random Experiments Random Experiments Remarks: The word "experiment"means a process of observation or measurement in a broad sense.It is not necessarily a real experiment as encountered in (e.g.)physics. 000 Experiments Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 5/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 5/248 Remarks: ● The word "experiment" means a process of observation or measurement in a broad sense. It is not necessarily a real experiment as encountered in (e.g.) physics. Random Experiments Foundation of Probability Theory Random Experiments