Suppose we roll a fair die with each of the numbers

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Unformatted text preview: hem. Before we state the axioms, we discuss a very simple example to introduce some terminology. Suppose we roll a fair die, with each of the numbers one through six represented on a face of the die, and observe which of the numbers shows (i.e. comes up on top when the die comes to rest). There are six possible outcomes to this experiment, and because of the symmetry we declare that each should have equal probability, namely, 1/6. Following tradition, we let Ω (pronounced “omega”) denote the sample space, which is the set of possible outcomes. For this example, we could take Ω = {1, 2, 3, 4, 5, 6}. Performing the experiment of rolling a fair die corresponds to selecting an outcome from Ω. An event is a subset of Ω. An event is said to occur or to be true when the experiment is performed if the outcome is in the event. Each event A has an associated probablilty, P (A). For this experiment, {1} is the event that one shows, and we let P ({1}) = 1/6. For brevity, we write this as P {1} = 1/6. Similarly, we let P {2} = P {3} = P {4} = P {5} = P {6} = 1/6. But...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

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