Chapter6_STAT1100.ppt", filename="Chapter6_STAT1100.ppt", filename="Chapter6_STA

Chapter6_STAT1100.ppt", filename="Chapter6_STAT1100.ppt", filename="Chapter6_STA

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Probability Statistics for Management and Economics Chapter 6
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Objectives Assigning Probability to Events Joint, Marginal, and Conditional Probability Probability Rules and Trees Bayes’ Law Identifying the Correct Method
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Probability Chance There’s a 99% chance that we’ll discuss Probability in today’s class Critical component of statistical inference Used for decision making
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Random Experiment A random experiment is an action or process that leads to one of several possible outcomes. For example: Experiment Outcomes Flip a coin Heads, Tails Exam Marks Numbers: 0, 1, 2, . .., 100 Assembly Time t > 0 seconds Course Grades F, D, C, B, A, A+
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Probabilities List the outcomes of a random experiment… This list must be exhaustive , i.e. ALL possible outcomes included. Die roll {1,2,3,4,5} Die roll {1,2,3,4,5,6} The list must be mutually exclusive , i.e. no two outcomes can occur at the same time: Die roll {odd number or even number} Die roll{ number less than 4 or even number}
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Sample Space A list of exhaustive and mutually exclusive outcomes is called a sample space and is denoted by S. The outcomes are denoted by O 1 , O 2 , …, O k Using notation from set theory, we can represent the sample space and its outcomes as: S = {O 1 , O 2 , …, O k }
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Requirements of Probabilities Given a sample space S = {O 1 , O 2 , …, O k }, the probabilities assigned to the outcome must satisfy these requirements: (1) The probability of any outcome is between 0 and 1 i.e. 0 ≤ P(O i ) ≤ 1 for each i , and (1) The sum of the probabilities of all the outcomes equals 1 ) + P(O 2 ) + … + P(O k ) = 1 P(O i ) represents the probability of outcome i
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Approaches to Assigning Probabilities Classical approach : make certain assumptions (such as equally likely, independence) about situation. Relative frequency : assigning probabilities based on experimentation or historical data. Subjective approach : Assigning probabilities based on judgment or prior experience
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Classical Approach If an experiment has n possible outcomes, this method would assign a probability of 1/ n to each outcome. Experiment: Rolling a die Sample Space: S = {1, 2, 3, 4, 5, 6} Probabilities: Each sample point has a 1/6 chance of occurring.
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Classical Approach Experiment: Rolling dice Sample Space: S = {2, 3, …, 12} Probability Examples: P(10) = 3/36 P(6) = 5/36 P(2) = 1/36 1 2 3 4 5 6 1 2 3 4 5 6 7 5 6 7 8 3 4 5 6 7 8 9 8 9 10 9 10 11 6 7 8 9 10 11 12 What are the underlying,  unstated assumptions??
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Relative Frequency Approach Bits & Bytes Computer Shop tracks the number of desktop computer systems it sells over a month (30 days): For example, 10 days out of 30 From this we can construct the probabilities of an event (i.e. the # of desktop sold on a given day)… Desktops Sold # of Days 0 1 1 2 2 10 3 12 4 5
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Relative Frequency Approach Desktops Sold # of Days Desktops Sold 0 1 1/30 = .03 1 2 2/30 = .07 2 10 10/30 = .33 3 12 12/30 = .40 4 5 5/30 = .17  ∑ = 1.00 “There is a 40% chance Bits & Bytes will sell 3 desktops on any given day”
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Subjective Approach “In the subjective approach we define
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This note was uploaded on 06/25/2008 for the course BUSSPP MCE taught by Professor Atkins during the Spring '08 term at Pittsburgh.

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Chapter6_STAT1100.ppt", filename="Chapter6_STAT1100.ppt", filename="Chapter6_STA

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