What Is a Random Variable?

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A random variable assigns a number to each outcome of a random circumstance, or, equivalently, a random variable assigns a number to each unit in a population. It is easier to create rules for broad classes of situations and then identify how a specific example fits into a class than it is to create rules for each specific example. We can employ this strategy quite effectively for working with a wide variety of situations Involving probability and random outcomes. We categorize these situations by defining a generic numerical outcome, or "random variable." for similar random circumstances. Identifying the type of random variable ap¬propriate in a given situation makes it easy to find probabilities and other infor¬mation that would be difficult to derive from first principles. There are two different broad classes of random variables:

1.A continuous random variable can take any value in an interval or col¬lection of intervals. 2.A discrete random variable can take one of a countable list of distinct values.

Sometimes a random variable fits the technical definition of a dis¬crete random variable but it is more convenient to treat it as a continuous random variable. Examples include Incomes, prices, and exam scores. Sometimes continuous random variables are rounded off to whole units, giving the appearance of a discrete random variable, such as age in years or pulse rate to the nearest beat. In most of these situations, the num¬ber of possible values is large and we are more interested in probabilities concerning intervals than specific values, so the methods for continuous random variables will be used. We can consider discrete and continuous random variables separately because probabilities are computed and used differently for them. For discrete random variables, we are interested in probabilities of exact outcomes or a series of them. For continuous random variables, we are Interested in the probability of the outcome...
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