Since these events both involve the outcome of a

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Unformatted text preview: o events. It does not make sense to say that a single event A is independent, without reference to some other event. If the experiment underlying the probability space (Ω, F , P ) involves multiple physically separated parts, then it is intuitively reasonable that an event involving one part of the experiment should be independent of another event that involves some other part of the experiment that is physically separated from the first. For example, when an experiment involves the rolls of two fair dice, it is implicitly assumed that the rolls of the two dice are physically independent, and an event A concerning the number showing on the first die would be physically independent of any event concerning the number showing on the second die. So, often in formulating a model, it is assumed that if A and B are physically independent, then they should be independent under the probability model (Ω, F , P ). 2.4. INDEPENDENCE AND THE BINOMIAL DISTRIBUTION 31 The condition for A to be independent of B, namely P (AB ) = P (A)P (B )...
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