Probabilità/Ripasso di matematica: differenze tra le versioni
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We note that <math>\Omega^c = \emptyset</math>.
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==Elementary Set Operations==
<!-- Probability theory makes extensive use of elementary set operations.
Below, we review the ideas of set theory, and establish the basic terminology and notation.
Consider two sets, S and T.
Riga 124:
The index set I can be finite or even infinite.
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==Rules of Set Theory==
<!-- Given a collection of sets, it is possible to form new ones by applying elementary set operations to them.
As in algebra, one uses parentheses to indicate precedence.
For instance, <math>R \cup (S \cap T)</math> denotes the union of two sets R and <math>S \cap T</math>, while <math>(R \cup S) \cap T</math> represents the intersection of two sets <math>R \cup S</math> and <math>T</math>.
Riga 176:
The second law can be obtained in a similar fashion.
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==Cartesian Products==
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It involves the notion of an ''ordered pair'' of objects.
Given sets S and T, the ''cartesian product'' S x T is the set of all ordered pairs (x, y) for which x is an element of S and y is an element of T,
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== Summary of Probability & Set Theory ==
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