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Published in:
2017 | OriginalPaper | Chapter
3. Continuous Random Variables and Probability Distributions
Authors : Matthew A. Carlton, Jay L. Devore
Published in: Probability with Applications in Engineering, Science, and Technology
Publisher: Springer International Publishing
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Abstract
As mentioned at the beginning of Chap. 2, the two important types of random variables are discrete and continuous. In this chapter, we study the second general type of random variable that arises in many applied problems. Sections 3.2 and 3.3 present the basic definitions and properties of continuous random variables, their probability distributions, and their various expected values. The normal distribution, arguably the most important and useful model in all of probability and statistics, is introduced in Sect. 3.4. Sections 3.5 and 3.6 discuss some other continuous distributions that are often used in applied work. In Sect. 3.7, we introduce a method for assessing whether given sample data is consistent with a specified distribution. Section 3.8 presents methods for obtaining the distribution of a rv Y from the distribution of X when the two are related by some equation Y = h(X). The last section of this chapter is dedicated to the simulation of continuous rvs.