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10 Lecture 3 - Probability

# 10 Lecture 3 - Probability - Lecture3 MeasuresofVariation...

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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!
Quiz 1! Duration: 30 minutes

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Let’s take 10 to relax…

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The Basics of Probability
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
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
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?”
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:
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