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Two random variables with the same probability distribution can still differ in terms of their associations with, or [[independence (probability theory)|independence]] from, other random variables. The realizations of a random variable, that is, the results of randomly choosing values according to the variable's probability distribution function, are called [[random variate]]s.
Although the idea was originally introduced by [[Christiaan Huygens]], the first person to think systematically in terms of random variables was [[Pafnuty Chebyshev]].<ref>{{Cite web|title=Christiaan Huygens {{!}} Encyclopedia.com|url=https://www.encyclopedia.com/people/science-and-technology/physics-biographies/christiaan-huygens|access-date=2021-03-12|website=www.encyclopedia.com}}</ref><ref>{{cite journal|journal=BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY|volume=3|number=1|date=July 1980|title=HARMONIC ANALYSIS AS THE EXPLOITATION OF SYMMETRY - A HISTORICAL SURVEY|author=George Mackey}}</ref>
==Definition==
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