Foundation of Probability Theory Basic Concepts of Probability Basic Concepts of Probability Remarks: A sample space S is sometimes called an outcome space. Each outcome in S is called an element of S,or simply a sample point. Sample Point Sample Space It is important to note that tor a random experiment, one knows the set of all possible basic outcomes,but one does not know which outcome will arise before performing the random experiment. Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 11/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 11/248 Remarks: ● A sample space S is sometimes called an outcome space. Each outcome in S is called an element of S, or simply a sample point. ● It is important to note that for a random experiment, one knows the set of all possible basic outcomes, but one does not know which outcome will arise before performing the random experiment. Basic Concepts of Probability Foundation of Probability Theory Basic Concepts of Probability
Foundation of Probability Theory Basic Concepts of Probability Basic Concepts of Probability Example 1:Throwing a Coin Head(H) Tail(T)】 十 Two possible outcomes: The sample space is S=H,T} Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 12/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 12/248 Example 1: [ Throwing a Coin ] Two possible outcomes: Basic Concepts of Probability Foundation of Probability Theory Basic Concepts of Probability 𝑆 = {𝐻, 𝑇} Head(H) Tail(T) The sample space is
Foundation of Probability Theory Basic Concepts of Probability Basic Concepts of Probability Example 2:Direction of Changes Let Y 1 if the U.S.Gross Domestic Product(GDP) growth rate is positive and Y =0 if the U.S.GDP growth rate is negative. Real GDP Growth Percent Actual Projected 2000 2004 2008 2012 2016 2020 2024 2028 Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 13/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 13/248 Example 2: [ Direction of Changes ] Let 𝑌 = 1 if the U.S. Gross Domestic Product (GDP) growth rate is positive and 𝑌 = 0 if the U.S. GDP growth rate is negative. Basic Concepts of Probability Foundation of Probability Theory Basic Concepts of Probability
Foundation of Probability Theory Basic Concepts of Probability Basic Concepts of Probability Example 3:Rolling a Die The basic outcomes are the numbers 1,2,3,4,5,6. Single Die Sample Space S={1,2,3,4,5,6} 6 outcomes Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 14/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 14/248 Example 3: [ Rolling a Die ] The basic outcomes are the numbers 1, 2, 3, 4, 5, 6. Basic Concepts of Probability Foundation of Probability Theory Basic Concepts of Probability 𝑆 = {1,2,3,4,5,6}
Foundation of Probability Theory Basic Concepts of Probability Basic Concepts of Probability Example 4:Throwing Two Coins The sample space H HH H T HT Outcome H TH T TT S=(HH,HT.TH,TT) Sample Space S={H,H),H,T),(T,H),(T,T} Foundation of Probability Theory Introduction to Statistics and Econometrics May22,2019 15/248
Foundation of Probability Theory Introduction to Statistics and Econometrics May 22, 2019 15/248 Example 4: [ Throwing Two Coins ] The sample space Basic Concepts of Probability Foundation of Probability Theory Basic Concepts of Probability 𝑆 = { 𝐻, 𝐻 , 𝐻, 𝑇 , 𝑇, 𝐻 , (𝑇, 𝑇)}