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# Lect8v4_1up - Stat 104 Quantitative Methods for Economists Class 8 Introduction to Probability Part I 1 What is probability Probability is a

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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 ? s Probability is a measure of uncertainty. s We can try to compute the probability of almost any event of interest. n ven is the basic element to which 2 s An even t is the basic element to which probability can be applied; it is the result of an observation or experiment, or the description of some potential outcome.
Some examples of events Example events we can assign probability to: s Getting a head when we flip a coin oca ola stock rises 5% next week 3 s Coca-Cola stock rises 5% next week s 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: ill our new product be successful ? 4 s Will our new product be successful ? s How many yen will a dollar buy in currency markets a month from today? s Will the manufactured part be defective ? s Given you took a test drive, will you buy the car ?
Most people don’t get probability s Unfortunately, most people do not attempt to evaluate probability in a quantitative way. Instead, they rely on intuition, doubtful logic, misinterpreted experience, and emotion. 5 s As the famous American jurist, Oliver Wendell Holmes, put it: Most people think dramatically, not quantitatively. s 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 s We denote the probability of the event A as Prob(A), which we often abbreviate as Pr(A) or simply P(A). s The probability of the event A is the chance that A will occur. Hence probabilities range from 0 (no 6 chance of occurrence) to 1 (absolute chance of occurrence (a sure thing)).
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
By the Way, How is Probability Defined? s We all know that the probability of getting a head when I flip a coin is 0.5. s 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 ? s Where do probabilities come from ? 9

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Three “Types” of Probability s 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 b 1) Classical Approach b 2) Relative Frequency Approach b 3) Subjective Approach 10
But the rules are the same……. .

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## This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.

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Lect8v4_1up - Stat 104 Quantitative Methods for Economists Class 8 Introduction to Probability Part I 1 What is probability Probability is a

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