lec2 - Wednesday, 12nd 1. Review Outcome ( ) , Sample space...

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Unformatted text preview: Wednesday, 12nd 1. Review Outcome ( ) , Sample space () , Event ( E ) Example: Consider a playo series (maximum 7 games) between the L.A. Lakers and Boston Celtics. In terms of winning-lose (LA-BOS) scores, the sample space consists of outcomes = { (4 , 0) , (4 , 1) , (4 , 2) , (4 , 3) , (3 , 4) , (2 , 4) , (1 , 4) , (0 , 4) } THe even that the Celtics wins at least two games is then E = { (0 , 4) , (1 , 4) , (2 , 4) , (3 , 4) , (4 , 3) , (4 , 2) } 2. Probability A nite meausre that takes event E as input and converts it to output, P ( E ) , i.e. P : F [0 , 1] where F is a nice collection of events, mathematically, it is called the - algebra of . Example: Consider the event S (a successful transimission de ned earlier). From experience with the network provider, the chance that the next message gets through is 95%, then we write P ( S ) = . 95 = 95% . To be able to work with probabilities, in particu- lar, to be able to compute probabilities of event, a mathematical foundation is needed set theory. 3. Sets and Venn Diagrams A set is a collection of distinct objects, considered as an object in its own right. An event can usually be abstracted as a set. 1 1. Review symbols ,/ , , , , : e.g. if a is a member of B, then a B ; if every member of set A is also member of set B, then A is said to be a subset of B, i.e. A B (A is contained in B); A B and B A implies A = B . Exampls: 2. Empty set is a set having no elements, in some situation denoted by {} ....
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lec2 - Wednesday, 12nd 1. Review Outcome ( ) , Sample space...

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