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Unformatted text preview: Principles of Statistics 1 Lecture 3: Math 203 Abbas Khalili Department of Mathematics and Statistics McGill University May 04, 2011 Principles of Statistics 1 Lecture 3: Math 203 – p. 1/6 Chapter 3 PROBABILITY Principles of Statistics 1 Lecture 3: Math 203 – p. 2/6 Introduction Chapter 2: In STATISTICS we use the data to make decisions about a population of interest. Chapter 3: In PROBABILITY we use information about the population to (infer or) make decisions about a sample. Principles of Statistics 1 Lecture 3: Math 203 – p. 3/6 Introduction An easy definition: Probability is a way of expressing knowledge or belief that an event will occur or has occurred. In almost every day conversation we use the terms: chance or probability . Examples : what is the chance that tomorrow is a rainy day? what is the chance that we observe a head when tossing a fair coin? Principles of Statistics 1 Lecture 3: Math 203 – p. 4/6 Basics concepts in probability theory Experiment : an act or process of observation that leads to a single outcome that cannot be predicted with certainty. tossing a coin: outcome would be head or tail. selecting a numbered ball from { B 1 ,B 2 ,...,B 50 } . A sample point : one particular outcome of an experiment. Sample space : the collection of all possible outcomes of an experiment. We use S to represent a sample space. Principles of Statistics 1 Lecture 3: Math 203 – p. 5/6 Example 1 Experiment: rolling two sixsided fair dice Principles of Statistics 1 Lecture 3: Math 203 – p. 6/6 Example 1 Experiment: rolling two sixsided fair dice Give an example of a sample point of the experiment: Principles of Statistics 1 Lecture 3: Math 203 – p. 6/6 Example 1 Experiment: rolling two sixsided fair dice Give an example of a sample point of the experiment: a 2 on the first die, and a 5 on the second die. Principles of Statistics 1 Lecture 3: Math 203 – p. 6/6 Example 1 Experiment: rolling two sixsided fair dice Give an example of a sample point of the experiment: a 2 on the first die, and a 5 on the second die. What is the sample space? S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6) (2,1), (2,2), (2,3), (2,4), (2,5), (2,6) (3,1), (3,2), (3,3), (3,4), (3,5), (3,6) (4,1), (4,2), (4,3), (4,4), (4,5), (4,6) (5,1), (5,2), (5,3), (5,4), (5,5), (5,6) (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} Principles of Statistics 1 Lecture 3: Math 203 – p. 6/6 Example 1 Experiment: rolling two sixsided fair dice Give an example of a sample point of the experiment: a 2 on the first die, and a 5 on the second die. What is the sample space? S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6) (2,1), (2,2), (2,3), (2,4), (2,5), (2,6) (3,1), (3,2), (3,3), (3,4), (3,5), (3,6) (4,1), (4,2), (4,3), (4,4), (4,5), (4,6) (5,1), (5,2), (5,3), (5,4), (5,5), (5,6) (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} The sample space has 36 sample points....
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 Summer '08
 Dr.JoseCorrea
 Math, Statistics, Probability, Probability theory, Department of Mathematics and Statistics

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