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UNIT11

# UNIT11 - Unit 11 Probability and Calculus I Discrete...

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Unit 11 Probability and Calculus I Discrete Distributions Terminology: Each problem will concern an experiment , which can result in any one of a number of outcomes . The set consisting of all possible outcomes of an experiment is called the sample space, S , of the experiment. For a set, A , | A | is the number of elements in A (the size of A ). Any collection of outcomes ( i.e. any subset of the sample space) will be called an event . Associated with each event is a number between 0 and 1 called its probability , which measures the likelihood of the event occuring when the experiment is performed. Theorem 12.1. If E is an event, S the sample space then the probability associated with E , denoted Prob ( E ) is given by Prob ( E ) = | E | | S | where | E | is the number of elements in the event and | S | is the number of elements in the sample space. Example 1. If an experiment consists of tossing a fair die, then Sample Space = { 1 , 2 , 3 , 4 , 5 , 6 } = S and | S | = 6 1

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Some events : roll an even number = { 2 , 4 , 6 } = A then | A | = 3 roll an odd number = { 1 , 3 , 5 } = B then | B | = 3
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