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2 Discrete Random Variables Contents 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. 2.8. Basic Concepts . . . . . . . . . . . . Probability Mass Functions . . . . . . Functions of Random Variables . . . . . Expectation, Mean, and Variance . . . . Joint PMFs of Multiple Random Variables Conditioning . . . . . . . . . . . . . Independence . . . . . . . . . . . . . Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p. 2 . p. 4 . p. 9 p. 11 p. 22 p. 27 p. 36 p. 42 1 2 Discrete Random Variables Chap. 2 2.1 BASIC CONCEPTS In many probabilistic models, the outcomes are of a numerical nature, e.g., if they correspond to instrument readings or stock prices. In other experiments, the outcomes are not numerical, but they may be associated with some numerical values of interest. For example, if the experiment is the selection of students from a given population, we may wish to consider their grade point average. When dealing with such numerical values, it is often useful to assign probabilities to them. This is done through the notion of a random variable, the focus of the present chapter. Given an experiment and the corresponding set of possible outcomes (the sample space), a random variable associates a particular number with each outcome; see Fig. 2.1. We refer to this number as the numerical value or the experimental value of the random variable. ...
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Nightingale College Nature and Origins of Islam Religion Summary

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