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.
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© 1995 Springer Science+Business Media New York
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Isaac, R. (1995). Breaking Sticks, Tossing Needles, and More: Probability on Continuous Sample Spaces. In: The Pleasures of Probability. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0819-8_11
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DOI: https://doi.org/10.1007/978-1-4612-0819-8_11
Publisher Name: Springer, New York, NY
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