Abstract
Recall that two events A and B are independent if knowledge that B has occurred does not change the probability that A will occur: that is, P(A|B)=P(A). This of course is algebraically equivalent to the statement P(A∩B=P(A)P(B). The latter expression generalizes easily to a finite number of events: A1,….,A n are independent if P(A∩i=JA i =Π i = J P(A i ) for every subset J of {1,…,n|n| (see Definition 3.1)
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© 2004 Springer-Verlag Berlin Heidelberg
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Jacod, J., Protter, P. (2004). Independent Random Variables. In: Probability Essentials. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55682-1_10
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DOI: https://doi.org/10.1007/978-3-642-55682-1_10
Publisher Name: Springer, Berlin, Heidelberg
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