Abstract: The usefulness of the random variable concept depends upon the ability to determine the probability that the values of the random variable occur in a given set of real numbers. Probability distributions is meant to suggest that the most important property of a random variable X is how it "distributes probability." That is, how the probability associated with values of X is distributed over these values. For a discrete random variable the most convenient way to do this is an analytical formula for the probability mass function. This chapter discusses some discrete and continuous random variables that have been found to be especially useful in applied probability theory and of special importance to computer science applications. Each of these random variables is determined by either one or two parameters, that is, given the parameter or parameters, the entire probability distribution is known. This makes it relatively easy to fit one of these distributions to an empirical distribution. The chapter discusses the central limit theorem and some of its applications. The basic idea of the theorem is that the sum of independent random variables tends toward a normal random variable under very weak restrictions. This explains the special importance of the normal distribution. The chapter presents Several examples of the use of the central limit theorem.
Publication Year: 1978
Publication Date: 1978-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 4
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