QMM240-W08-IntroToProbability

QMM240-W08-IntroToProbability - QMM240 W08 Introduction to...

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QMM240 W08 Introduction to Probability Statistical Methods for Business I - Lecture Notes Page: 1 Introduction to Probability Outline : Why Probability? Probability Definitions Probability Rules I) Why Probability? 1) The business world is uncertain a) Daily demand for some product b) Cost of some supply over time c) Waiting times of customers at service centers d) Time to produce some product or complete some project 2) In business we make decisions under uncertainty a) Where to open a new plant, how much to invest, how much capacity, who to hire, how much to bid on a project, due date quoting, sc heduling, and on and on… 3) Need a language for talking about uncertainty 4) Need a method to quantify uncertainty 5) Learn to use probability to build models to support managerial decision making 6) Modeling and analysis 7) Probability helps us make predictions about the future a) A bit like weather forecasting
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QMM240 W08 Introduction to Probability Statistical Methods for Business I - Lecture Notes Page: 2 II) Probability Definitions Random Experiment An observational process whose outcome cannot be known in advance Experimental trial is an act or process leading to a single outcome Outcome has some uncertainty Can not predict correct outcome 100% of the time Randomness is a negative property absence of pattern To ponder: How does Excel or other computer programs generate random numbers? What kinds of patterns in a string of numbers might indicate that they were NOT random? A random (or stochastic) process is a repeatable random experiment EXAMPLES: Flipping a coin Rolling a die Demographics of one randomly selected person A visitor to Amazon.com may or may not make a purchase Outcome or Sample Point Unique result of an experiment EXAMPLES: Coin lands heads up, Rolling a three with a die A Michigan resident Amazon.com visitor makes a purchase Sample Space: S Collection of all possible outcomes Population S is a set.
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QMM240 W08 Introduction to Probability Statistical Methods for Business I - Lecture Notes Page: 3 [Notation] Often use {} to enclose list of elements in S Discrete Sample Space Number of outcomes is countable (can find a one to one mapping between the integers and the outcomes) An infinitely countable number of outcomes acceptable EXAMPLE: The number of brokerage accounts managed by Fidelity EXAMPLES: Number of additional games won by a team that makes it to the 2 nd stage (16 teams) of the FIFA World Cup The identity of the first case chosen in Deal or No Deal (in US) The number of other firms submitting competing bids on a project The result of two flips of a fair coin 1 2 3 4 5
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QMM240 W08 Introduction to Probability
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