Foundation of Probability Theory Random Experiments Random Experiments Remarks: There are two essential elements of a random experiment: The set of all possible outcomes; The likelihood with which each outcome will occur. Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 6/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 6/248 Remarks: ● There are two essential elements of a random experiment: Random Experiments Foundation of Probability Theory Random Experiments The set of all possible outcomes; The likelihood with which each outcome will occur
Foundation of Probability Theory Random Experiments Random Experiments Remarks: The purpose of mathematical statistics is to provide mathematical models for random experiments of interest. Once a model for such an experiment is provided and the theory worked out in detail,the statistician may, within this framework,make inference about the probability law of the random experiment. Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 7/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 7/248 Remarks: ● The purpose of mathematical statistics is to provide mathematical models for random experiments of interest. ● Once a model for such an experiment is provided and the theory worked out in detail, the statistician may, within this framework, make inference about the probability law of the random experiment. Random Experiments Foundation of Probability Theory Random Experiments
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 8/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 8/248 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 Basic Concepts of Probability Basic Concepts of Probability Definition 2.Sample Space The possible outcomes of a random experiment are called "basic outcomes",and the set of all basic outcomes constitutes "the sample space",which is denoted by S. Flipping a Coin Rolling a Six Sided Dice Spinning a 4 color spinner Rolling a Weighted Dice 6 red yellow 545 6 blue green 6 SAMPLE SPACE SAMPLE SPACE SAMPLE SPACE SAMPLE SPACE Head,Tail} {1,2,3,4,5,6} (Red,Yellow,Green,Blue} {4,5,6 Uniform Uniform Uniform Not Uniform Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 9/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 9/248 Basic Concepts of Probability Foundation of Probability Theory Basic Concepts of Probability Definition 2. [ Sample Space ] The possible outcomes of a random experiment are called "basic outcomes", and the set of all basic outcomes constitutes "the sample space", which is denoted by S
Foundation of Probability Theory Basic Concepts of Probability Basic Concepts of Probability When an experiment is performed,the realization of the experiment will be one (and only one)outcome in the sample space. If the experiment is performed a number of times,a different outcome may occur each time or some outcomes may repeat. Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 10/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 10/248 Basic Concepts of Probability Foundation of Probability Theory Basic Concepts of Probability ● When an experiment is performed, the realization of the experiment will be one (and only one) outcome in the sample space. ● If the experiment is performed a number of times, a different outcome may occur each time or some outcomes may repeat