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Breaking Sticks, Tossing Needles, and More: Probability on Continuous Sample Spaces

  • Richard Isaac
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Up to now, we have been working with discrete sample spaces and discrete random variables (see Chapters 1 and 7). There are problems, however, for which a discrete sample space is not appropriate because there are just too many possible outcomes. Suppose, for instance, that I want to choose a number on the interval between 0 and 1 “at random.” Ignoring for a moment exactly what I mean by the term “at random” in this context, we note that the number chosen can be any value on the interval, so there is a continuum of possible values. This continuum has so many numbers in it that they cannot all be counted off using the positive integers; for this reason the sample space of this interval is not discrete but is what is called a continuous sample space.

Keywords

Sample Space Number Line Equilateral Triangle Unit Interval Discrete Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Richard Isaac
    • 1
    • 2
  1. 1.Department of MathematicsLehman College, City University of New YorkBronxUSA
  2. 2.The Graduate CenterNew YorkUSA

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