2303 11 1 prob and bayes

2303 11 1 prob and bayes - Using Probability and Bayes...

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Using Probability and Bayes Using Probability and Bayes Theorem Theorem ©

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Outcomes After studying this material, you should be able to: Understand the three approaches to assessing probabilities. Apply the common rules of probability including Bayes Theorem.
Probability Assessing Probability Events Combining Events A “OR” B A “given” B A “AND” B Bayes Theorem.

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Probability Probability Probability refers to the chance that a refers to the chance that a particular event will occur. particular event will occur. The probability of an event will be a value in the range 0.00 to 1.00. A value of 0.00 means the event will not occur. A probability of 1.00 means the event will occur. Anything between 0.00 and 1.00 reflects the uncertainty of the event occurring. Probability P 0 1
PROBABILITY RULE 1 PROBABILITY RULE 1 0 . 1 0 P The Rules of Probability This isn’t rocket science.

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Assessing Probabilities Theoretical: Number of Possibilities Relative Frequency: Empirical Subjective
Theoretical Probability Assessment Theoretical Probability Assessment Theoretical Probability Assessment refers to the method of determining probability based on the ratio of the number of ways the event of interest can occur to the total number of ways any event can occur.

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THEORETICAL PROBABILITY MEASUREMENT THEORETICAL PROBABILITY MEASUREMENT Theoretical Probability Assessment occur can anything ways of number Total occur can E ways of Number ) P(E i i =
The Canadian Census of 2006 Source: http://www40.statcan.gc.ca/l01/cst01/famil123a-eng.htm Telemarketers call people in Halifax in 2006 at random to sell products designed for family households. We can calculate the probability that the household will be of that type by dividing the number of people in that type of household by the total number of people: 305,090/367,975 = 0.829. Telemarketing in Halifax

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Relative Frequency of Occurrence (Empirical Probability) Relative Frequency of Occurrence Relative Frequency of Occurrence refers to a method that defines probability as the number of times an event occurs, divided by the total number of times an experiment is performed in a large number of trials. E.g. Results of a survey: Out of 100 respondents, 50 said they preferred Pepsi to Coke
Relative Frequency of Occurrence Example On a production line products are tested throughout a day. Out of 10000 products, 52 are found to be defective. Probability of defective product = 52/10000 = 0.52%

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Law of Large Numbers (LLN) If the events are independent, then as the number of trials increases, the long-run relative frequency of an event gets closer and closer to a single value.
Subjective (Personal) Probability Assessment Subjective Probability Assessment Subjective Probability Assessment refers to the method that defines probability of an event as reflecting a decision maker’s state of mind regarding the chances that the particular event will occur.

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This note was uploaded on 10/10/2011 for the course ADM 2303 taught by Professor Brand during the Fall '11 term at University of Ottawa.

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2303 11 1 prob and bayes - Using Probability and Bayes...

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