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lect8v4_1up - Stat 104 Quantitative Methods for Economists...

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Stat 104: Quantitative Methods for Economists Class 8: Introduction to Probability, Part I 1
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What is probability ? square6 Probability is a measure of uncertainty. square6 We can try to compute the probability of almost any event of interest. square6 An even t is the basic element to which 2 probability can be applied; it is the result of an observation or experiment, or the description of some potential outcome.
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Some examples of events Example events we can assign probability to: square6 Getting a head when we flip a coin square6 Coca-Cola stock rises 5% next week 3 square6 Ford will produce a hybrid SUV that gets 50mpg by 2012. What are some additional events you could define for the above scenarios ?
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Probability is important Probability is useful to study since uncertainty plays a major role in economic decisions: square6 Will our new product be successful ? 4 square6 How many yen will a dollar buy in currency markets a month from today? square6 Will the manufactured part be defective ? square6 Given you took a test drive, will you buy the car ?
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Most people don’t get probability square6 Unfortunately, most people do not attempt to evaluate probability in a quantitative way. Instead, they rely on intuition, doubtful logic, misinterpreted experience, and emotion. square6 As the famous American jurist, Oliver Wendell 5 Holmes, put it: Most people think dramatically, not quantitatively. square6 This section should help you start thinking about probability (uncertainty) in a clearer fashion and hence make more informed decisions.
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Values of probabilities square6 We denote the probability of the event A as Prob(A), which we often abbreviate as Pr(A) or simply P(A). square6 The probability of the event A is the chance that A will occur. Hence probabilities range from 0 (no chance of occurrence) to 1 (absolute chance of 6 occurrence (a sure thing)).
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How is Probability Interpreted ? 0 1 7 Name some events that would go here Name some events that would go here Name some events that would go here Name some events that would go here
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The Birthday Problem Sometimes the results of using probability theory are surprising (to me at least). Suppose we have n people in a room (randomly selected, i.e. no twins). What is the probability that at least 2 people have the same birthday ? 8 n Prob(at least 2 people have same birthday) 15 25 40 50 70
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By the Way, How is Probability Defined? square6 We all know that the probability of getting a head when I flip a coin is 0.5. square6 What about the probability of a 35 year old white male who hasn’t smoked in 10 years of being diagnosed with lung cancer this year ? square6 Where do probabilities come from ? 9
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Three “Types” of Probability square6 There are three basic ways of classifying probability. These three represent rather different conceptual approaches to the study of probability theory; in fact, experts disagree about which approach is the proper one to use. The three approaches are boxshadowdwn 1) Classical Approach boxshadowdwn 2) Relative Frequency Approach boxshadowdwn 3) Subjective Approach 10
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But the rules are the same……..
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