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econ2500_-_chapter_4_-_pr.docx

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Department
Economics
Course
ECON 2500
Professor
All Professors
Semester
Winter

Description
Introductory Statistics for Economists ECON 2500 – Winter 2011 – Xianghong Li Chapter 4 – Probability: The Study of Randomness – Feb 15 4.1 Randomness - Deterministic event o E.g. my car won’t run without gas. - Example 1: random phenomena. - Random events o The outcome is uncertain before it occurs. o There is a regular pattern for possible outcomes in a large number of repetitions. (Not true for chaotic or haphazard events, such as earthquake). 4.2 Probability Models - A list of possible outcomes. - A probability for each outcome. Sample Space - Sample space S of a random phenomenon: the set of ALL possible outcomes. o E.g. tossing a coin once S = {H, T} o E.g. Do you favour mandatory retirement S = {Y, N} Event - Event: a set of outcomes of a random phenomenon. It is a subset of a sample space. o E.g. toss a fair coin twice:  Sample space S = ?  Event A: #heads = 1 Another Example - Toss a fair coin four times: o Using a tree structure to exhaust all possible outcomes. o Define the outcomes as number of heads, sample space? o Comment: the sample space depends on how we define individual outcome. Probabilities in a Finite Sample Space - Assign a probability to each individual outcome. These probabilities must be numbers between 0 and 1 and must have sum 1. - The probability of any event is the sum of the probabilities of the outcomes
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