lesson3 - Probability

lesson3 - Probability - Lesson3: ASurveyofProbability...

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 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson3-1 Lesson 3: A Survey of Probability  Concepts
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 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson3-2 Outline Learning Exercises Definitions Basic rules of Probability Independence Tree Diagram Bayes’ Theorem
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 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson3-3 Learning exercise 1:  University Demographics Current enrollments by college and by sex appear in the following  table.  College Ag-For Arts-Sci Bus-Econ Educ Engr Law  Undecl Totals Female 500 1500 400 1000 200 100 800 4500 Male 900 1200 500 500 1300 200 900 5500 Totals 1400 2700 900 1500 1500 300 1700 10000 If we select a student at random, what is the probability that the  student is : A female or male, i.e., P(Female or Male). Not from Agricultural and Forestry, i.e., P(not-Ag-For) A female given that the student is known to be from BusEcon, i.e.,  P(Female |BusEcon). A female and from BusEcon, i.e., P(Female and BusEcon). From BusEcon, i.e., P(BusEcon).
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 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson3-4 Learning exercise 1:  University Demographics College Ag-For Arts-Sci Bus-Econ Educ Engr Law  Undecl Totals Female 500 1500 400 1000 200 100 800 4500 Male 900 1200 500 500 1300 200 900 5500 Totals 1400 2700 900 1500 1500 300 1700 10000 P(Female or Male) =(4500 + 5500)/10000 = 1 P(not-Ag-For) =(10000 – 1400) /10000 = 0.86 P(Female | BusEcon) = 400 /900 = 0.44 P(Female and BusEcon) = 400 /10000 = 0.04 P(BusEcon) = 900 /10000 = 0.09 P(Female and BusEcon) = P(BusEcon) P(Female | BusEcon)
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 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson3-5 Learning exercise 2:  Predicting Sex of Babies Many couples take advantage of ultrasound exams to determine the  sex of their baby before it is born. Some couples prefer not to know  beforehand. In any case, ultrasound examination is not always  accurate. About 1 in 5 predictions are wrong.  In one medical group, the proportion of girls correctly identified is  9 out of 10, i.e., applying the test to 100 baby girls, 90 of the tests  will indicate girls. and  the number of boys correctly identified is 3 out of 4.  i.e., applying the test to 100 baby boys, 75 of the tests will indicate  boys. The proportion of girls born is 48 out of 100.  What is the probability that a baby predicted to be a girl actually turns  out to be a girl?   Formally, find P(girl | test says girl).
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 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson3-6 Learning exercise 2:  Predicting Sex of Babies P(girl | test says girl) In one medical group, the proportion of girls correctly identified is  9 out of 10 and  the number of boys correctly identified is 3 out of 4.  The proportion of girls born is 48 out of 100.  Think about the next 1000 births handled by this medical group.    480 = 1000*0.48 are girls 520 = 1000*0.52 are boys
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This note was uploaded on 09/06/2010 for the course ECON ECON1003 taught by Professor Paul during the Fall '09 term at HKU.

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lesson3 - Probability - Lesson3: ASurveyofProbability...

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