10 Lecture 3 - Probability

10 Lecture 3 - Probability - Lecture3:...

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Lecture 3: Measures of Variation &   Probability Measures of variation (from Lecture 2) Probability basics and rules Bayes’ theorem
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Business Statistics 2 © Copyright 2007,  Alex Shoumarov et al Agenda 1. Quiz 1 2. Announcements 3. Descriptive statistics 4. The basics of probability 5. The rules of probability 6. Bayes’ theorem New!
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Quiz 1! Duration: 30 minutes
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Let’s take 10 to relax…
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Business Statistics 5 © Copyright 2007,  Alex Shoumarov et al Announcements
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The Basics of Probability
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Business Statistics 7 © Copyright 2007,  Alex Shoumarov et al Some real questions Should we bother playing the lottery? Why do we flip a coin to decide a ‘toss- up’? How do we use the information from a  medical test?
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Business Statistics 8 © Copyright 2007,  Alex Shoumarov et al What is probability? The likelihood or chance, in numerical  terms, that an event will occur Serves as the link between sampling  and inference
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Business Statistics 9 © Copyright 2007,  Alex Shoumarov et al The probability formula To be revisited later… ( 29 ( 29 1 x P events possible all of number total x event of occurances possible of Number x P N 1 i i = = å =
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Business Statistics 10 © Copyright 2007,  Alex Shoumarov et al Probability and  possibility The probability of  certain  event is 1 The probability of an  impossible  event is 0 Anything in between is probable: I have a 1 in a million chance (1/1,000,000) to win  the lottery (we’ll calculate this more precisely later) I have 0.1 chance to get 100 in the exam There is a 50% chance of rain The sum of all probabilities is 1
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Business Statistics 11 © Copyright 2007,  Alex Shoumarov et al Some initial terminology 1. Random experiment  2. Elementary (or simple) event 3. Complex event (usually just ‘event’)  4. Sample space 
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Business Statistics 12 © Copyright 2007,  Alex Shoumarov et al 1. Random experiment Where do probabilities come from? A process whose outcome cannot be  predicted with certainty is called a  random experiment Examples:  Rolling a die Shooting a basketball Asking: “Is stats your favourite subject?”
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Business Statistics 13 © Copyright 2007,  Alex Shoumarov et al 2. Elementary event The most rudimentary results of a random  experiment are called  elementary events Irreducible  to any simpler constituents In a random experiment there are always  more than one elementary events What are the elementary events that  result from rolling a die?
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Business Statistics 14 © Copyright 2007,  Alex Shoumarov et al 3. Complex event Complex events  are reducible  to  simpler constituent events i.e. to elementary events Rolling a die: Elementary events: S = {1, 2, 3, 4, 5, 6} Complex events: S = {even, odd}  Even = {2, 4, 6}    Odd = {1, 3, 5}
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10 Lecture 3 - Probability - Lecture3:...

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