Econometrics Outline 1

Econometrics Outline 1 - 2.2. SAMPLE SPACES -An experiment...

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2.2. SAMPLE SPACES -An experiment is any process of observation or measurement. -The result one obtains from an experiment are called the outcome of the experiment. -The set of all possible outcomes of an experiment is called the sample space (S) . -Each outcome in a sample space is called an element of the sample space (or simply a sample point ) -If a sample space has a finite number of elements , we list the elements using the following notation: S = {H,T} S = {1,2,3,4,5,6} -If a sample space has a large or infinite number of elements, we describe the elements. For example, “S is the set of all x such that x is an automobile with a CB radio.” S = {x| x is an automobile with a CB radio} For example, “S is the set of odd positive integers” S = {2k+1| k=0,1,2…} -If a sample space can be matched one-to-one with whole numbers, it is said to be countable . A sample space with an infinite number of elements can be countable: S = {H, TH, TTH, TTTH, TTTTH,…} -If a sample space contains a finite number of elements or an infinite though countable number of elements, it is said to be discrete. -Some sample spaces are not discrete , meaning they do not contain a finite number of elements or an infinite number of elements which are countable. (For example, measuring the time of a chemical reaction) If a sample space consists of a continuum, such as all the points of a line segment or all the points in a plane, it is said to be continuous . 2.3. EVENTS -In many problems we are interested in results that are not given directly by a specific element of a sample space. Rather, the results will be a collection of elements within the sample space (a subset of the sample space). “By definition, an event is a subset of a sample space.” -In many problems of probability we are interested in events that are actually combinations of two or more events, formed by taking unions, intersections, and complements. -If
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This note was uploaded on 10/21/2010 for the course ECON 3210 taught by Professor Molinari during the Spring '07 term at Cornell.

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Econometrics Outline 1 - 2.2. SAMPLE SPACES -An experiment...

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