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Unformatted text preview: following two conditions but is otherwise arbitrary: 1 The set { X ≤ x } is an event for every x . (In the applications, we are interested in the probability that a random variable X takes values in a certain region R of the x axis – this mild restriction is mainly of mathematical interest.) 2 The probabilities of the events { X = ∞} and { X =∞} equal to 0: P { X = ∞} = and P { X =∞} = (i.e., although we allow X to be ∞ or∞ for some outcomes, we demand that these outcomes form a set with zero probability.) Example An urn contains 90 $ 1 bills, 9 $ 5 bills, and 1 $ 50 bill. Let the random variable X be the denomination of a bill that is selected at random from the urn. (a) Describe the underlying space S of this random experiment and specify the probabilities of its elementary events. (b) Describe the sample space of X , S X , and ﬁnd the probabilities for the various values of X ....
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This note was uploaded on 05/05/2010 for the course ECECS 5605 taught by Professor Dasilver during the Fall '08 term at Virginia Tech.
 Fall '08
 DASILVER

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