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Week 1 and 2 Lecture Notes.pdf

Week 1 and 2 Lecture Notes.pdf - Econ 102A Introduction to...

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Econ 102A Introduction to Statistical Methods for Social Scientists Stanford University Course Materials for Week 1 and Week 2 Professor Scott M. McKeon Autumn Quarter, 2017 - 18 © Scott M. McKeon All Rights Reserved
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Weeks 1 and 2 Goals: 1. Gaining practice in probability tree modeling. 2. Getting acquainted with Venn diagrams. 3. Learning to distinguish different types of probabilities. 4. Understanding probability as a state of belief as opposed to objective fact. 5. Learning the process of probability tree collapsing. 6. Learning the process of probability tree flipping. 7. Gaining practice in modeling real-world examples. 8. Learning Bayes’ Rule and its relation to probability tree flipping. 9. Learning how to model probabilistic independence.
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Econ 102A Statistical Methods for Social Scientists Weeks 1 and 2 Definitions 1. The sample space of a probabilistic situation is the collection of all possible outcomes. In a probability tree model, this amounts to the collection of all paths of the tree. 2. An event is a collection of outcomes of particular interest. In this way, events are subsets of sample spaces. 3. The union of Event A and Event B, denoted A B, are those outcomes in either Event A or Event B (or both). 4. The intersection of Event A and Event B, denoted A B or AB, are those outcomes in both Event A and Event B. 5. The complement of Event A, denoted A c or A , are those outcomes not in Event A. 6. Intersection probabilities describe the chance that a series of events happen. That is, the chance that both Event A and Event B happen is the intersection probability of Event A and Event B. With regard to notation, we have already introduced the intersection notation A B or AB. The notation for the probability of such intersections is consistent in that the intersection probability of Event A and Event B is notated as P(A B) or P(AB). 7. Upon learning new information, we may be inclined to change the probabilities we had initially assigned to events. Conditional probabilities are the (updated) probabilities that we arrive at upon incorporating the learned information. With regard to notation, the updated assessment of P(A) given that Event B has already happened is denoted as P(A | B) (where the vertical bar is read as the word “given”). 8. Tree collapsing is a procedure performed on a probability tree whereby two or more branches within a single tree stage are collapsed into a single branch. 9. Tree flipping is a procedure performed on a probability tree whereby two or more stages of a tree are interchanged or “flipped”, thereby creating a new chronology as to the overall order in which the stages unfold. Handout #1 Page 1 of 1
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Econ 102A Statistical Methods for Social Scientists Weeks 1 and 2 Worksheet 1. Imagine a television station which has just aired its first installment of a new television show which the network hopes will become a big success. After airing the show, the station then surveys a number of people who viewed the program to gain viewer response.
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