MAT 2377 Chapter Notes -Ob River, Mutual Exclusivity, Almost Surely

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De nition : a random experiment is an experiment or a process for which the outcome cannot be predicted with certainty. De nition : the sample space (denoted s) of a random experiment is the set of all possible outcomes. The notation x a means that x belongs to a. De nition: an event is a subset of the sample space. We say that e has occured if the observed outcome x is an element of e, that is x e. (the empty set) is called the impossible event. Note: the following operations allow us to represent some events in terms of other events. Union: e1 e2 occurs means e1 occurs, or e2 occurs, or both occur, e1 e2 en occurs means that at least. E1, e2, , en occurs. one of the events. Intersection: e1 e2 occurs means e1 occurs and e2 occurs, e1 e2 en occurs means that all of the events e1, e2, .

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