Probability

Probability - C22.0103: Statistics for Business Control:...

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Unformatted text preview: C22.0103: Statistics for Business Control: Regression and Forecasting Hong Luo Section 003, Spring 2009 Tue/Thu/Fri, 11:00 - 12:15pm, Tisch 200 Stern School of Business New York University PROBABILITY Introduction Probability of an Event Counting Rules Conditional Probability and Independence Conditional Probability and Bayes Theorem Expected Value Introduction Probability of an Event Counting Rules Conditional Probability and Independence Conditional Probability and Bayes Theorem Expected Value Risk and Uncertainty I Uncertainty : the lack of complete certainty, that is, the existence of more than one possibility. I Life is full of uncertainty I How likely is it that it will rain tomorrow? I How long will it take to get to JFK? I How likely is it that Apples stock price will go back above 100 by the end of June? I Were we a local mom & pop store, how likely is it that Walmart enter our market next year? I Many others... I Probability is used to measure uncertainty: a set of probabilities assigned to a set of possibilities. e.g. There is a 60% chance that it will rain tomorrow. These definitions come from How to Measure Anything: Finding the Value of Intangibles in Business by Doug Hubbard Risk and Uncertainty I Risk : a state of uncertainty where some of the possibilities involve a loss, catastrophe, or other undesirable outcome. I Risk plays an important role in our daily life I Investing in the stock market I Starting your own business I Whom to support in the presidential election (Joe Lieberman) I Starting a family I Bungee jumping I Many others... I Measurement of risk: a set of possibilities each with quantified probabilities and quantified losses. Example: There is a 40% chance that our business will lose half a million next year. Basic Concepts in Probability Theory I Experiment : an experiment is an act or process of observation that leads to a single outcome that cannot be predicted with certainty I Outcome : a possible state of the world I heads or tails in a coin toss; 1, 2, 3, 4, 5, or 6 in a die roll I Sample Space : a complete set of possible outcomes I { heads , tails } in a coin toss; { 1,2,3,4,5,6 } in a die roll I Probability (of an outcome): a measure of the likelihood attached to each outcome in the sample space. I P ( heads ) = P ( tails ) = 1 2 in a coin toss; P (1) = P (2) = = P (6) = 1 6 More on the Sample Space I Out of one experiment, depending on the kind of outcomes we are interested in, we need to define the sample space accordingly. E.g., toss two coins instead of one. What are the kind of outcomes that you are interested in? How do you define the sample space accordingly? Given the sample space defined, what is the probability of each outcome?...
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This note was uploaded on 11/07/2010 for the course ECON 0001 taught by Professor Kitsikopoulos during the Spring '08 term at NYU.

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Probability - C22.0103: Statistics for Business Control:...

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