# Lecture_03 - 1 ISE 690 Statistical Methods for Engineers...

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1 Industrial and Systems and Engineering Management Department Fall 15 Dilcu Helvaci Barnes (Email: ISE 690 Statistical Methods for Engineers Discrete Random Variables and Probability Distributions

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2 Random Variable In any experiment, there are numerous characteristics that can be observed or measured, but in most cases an experimenter will focus on some specific aspect or aspects of a sample. For example, a researcher may test a sample of components and record only the number that have failed within 1000 hours, rather than record the individual failure times.
3 Random Variable In general, each outcome of an experiment can be associated with a number by specifying a rule association (e.g., the number among the sample of ten components that fail to last 1000 hours or the total weight of baggage for a sample of 25 airline passengers). Such a rule association is called random variable. A variable because different numerical values are possible and random because the observed value depends on which of the possible experimental outcome results.

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4 Random Variable Definition : A random variable (rv), X, is a function defined on the sample space (S) of an experiment, where X assigns a unique real number to every outcome (O) in S (i.e., X(O) is a real number for any outcome O in S). In other words X is a random variable if X is a function that assigns a real numbered value to every possible event in a sample space of interest.
5 Example Let the experiment consist of tossing 3 fair coins. Then, S = {HHH, HTH, HHT, THH, HTT, THT, TTH, TTT}.

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• Fall '15
• DilcuBarnes
• Probability theory

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