2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCO An Experiment (i):all possible outcomes are known (ii):outcome is not predictable with certainty 4日·5,421手·300C0 Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES An Experiment 1 £i§µall possible outcomes are known 2 £ii§µoutcome is not predictable with certainty Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCO Some examples of experiments Egl:the sex of a newborn child-girl boy Eg2:the order of finish in a race among the 7 horses-1~7 Eg3:measureing(in hours)the lifetime of a transistor-0oo Eg4:tossing two dice-(ij):i,j=1,2,3,4,5,6 Eg5:daily variation of the Shanghai Composite Index-[-10%,10%] Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES Some examples of experiments 1 Eg1µthe sex of a newborn child)girl!boy 2 Eg2µthe order of finish in a race among the 7 horses)1∼7 3 Eg3µmeasureing(in hours) the lifetime of a transistor)0∼ ∞ 4 Eg4µtossing two dice)(i,j) :i,j=1,2,3,4,5,6 5 Eg5µdaily variation of the Shanghai Composite Index)[−10%, 10%] Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS sAXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCC 2、sample space The set,,of all possible outcomes(w)of a particular experiment is called the sample space for the experiment. Eg1:=fHead,Tail} 0Eg2:2={1,2,3.4,5,6} QEg3:2=[0,+∞] ⊙Eg4:2={0,1,2,…} 0Eg5:2=[-10%,10%] 4口·5,43手·3000 Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES 2!sample space 1 The set,Ω,of all possible outcomes(ω) of a particular experiment is called the sample space for the experiment. 2 Eg1µΩ={Head,Tail} 3 Eg2µΩ={1,2,3,4,5,6} 4 Eg3µΩ=[0,+∞] 5 Eg4µΩ = {0, 1, 2, · · · } 6 Eg5µΩ = [−10%, 10%] Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCC 3、random event random event E:a subset of random event E:a set consisting of possible outcomes of the experiment. 4口t9:13，元，2900 Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES 3!random event 1 random event Eµa subset of Ωß 2 random event Eµa set consisting of possible outcomes of the experimentß Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCO 3、random event random event E:a subset of random event E:a set consisting of possible outcomes of the experiment, 口t15,4211手3000 Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES 3!random event 1 random event Eµa subset of Ωß 2 random event Eµa set consisting of possible outcomes of the experimentß Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCC 3、random event E has occurred:the outcome of the experiment is contained in E two special events: (1)certain event--the point of dice is less than 8); i)impossible event-(the point of dice is 10) 4口t9:13，元，2900 Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES 3!random event 1 E has occurredµthe outcome of the experiment is contained in E 2 two special eventsµ £i§certain event))Ω£the point of dice is less than 8§¶ £ii§impossible event))φ£the point of dice is 10§ Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCO 3、random event E has occurred:the outcome of the experiment is contained in E two special events: (i)certain event--(the point of dice is less than 8): (ii)impossible event--(the point of dice is 10) 4口·5,431手·3000 Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES 3!random event 1 E has occurredµthe outcome of the experiment is contained in E 2 two special eventsµ £i§certain event))Ω£the point of dice is less than 8§¶ £ii§impossible event))φ£the point of dice is 10§ Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCC Examples 0 play a dice--2={1,2,3,4,5,6 event A=point is 1=1 event B=frolling an odd number=1,3.5 event C=point is more than 4=15.6 口5,43)4元，3000 Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES Examples 1 play a dice))Ω = {1, 2, 3, 4, 5, 6} 2 event A={point is 1}={1} 3 event B={rolling an odd number}={1,3,5} 4 event C={point is more than 4}={5,6} Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCC Examples ©play a dice--2={1,2,3,4,5,6} event A={point is 1}={1) event B=frolling an odd number=1,3.5 event C={point is more than 4=5.6) 4口45.43，手·3000 Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES Examples 1 play a dice))Ω = {1, 2, 3, 4, 5, 6} 2 event A={point is 1}={1} 3 event B={rolling an odd number}={1,3,5} 4 event C={point is more than 4}={5,6} Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCC Examples @play a dice--2={1,2,3,4,5,6} event A={point is 1}={1} event B=frolling an odd number={1,3,5} event C=point is more than 4)=15.6 口t5,3y元，30a0 Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES Examples 1 play a dice))Ω = {1, 2, 3, 4, 5, 6} 2 event A={point is 1}={1} 3 event B={rolling an odd number}={1,3,5} 4 event C={point is more than 4}={5,6} Xiaohan Yang Chapter 2 Axioms of Probability