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Concept of a Random Variable
Book chapter

Concept of a Random Variable

P. Mohana Shankar
Probability, Random Variables, and Data Analytics with Engineering Applications, pp 77-232
09 Feb 2021
DOI: https://doi.org/10.1007/978-3-030-56259-5_3

Abstract

Area under the ROC curve Cumulative distribution functions Densities Neyman-Pearson threshold Random variable Receiver operating characteristics curves (ROC) Transformation of random variables
The concept of a random variable and its importance in modeling the outcomes of experiments are presented. While providing traditional coverage of discrete and continuous random variables, densities, distribution functions, and conditional densities, readers are also introduced to mixed random variables as well as mixture densities to reflect the current trends in modeling of data from experiments. The examples of transformation of variables presented offer a peek into the various engineering applications. Unlike other books, data analytic techniques are presented again with the offering of receiver operating characteristic curves (ROC) and performance measures such as the area under the ROC curve (AUC), positive predictive values, etc., thereby relating the subject matter to the topics covered in Chap. 2. Chapter summary provided offers detailed descriptions of densities and their properties. Multiple examples of transformation of variables are also presented. Examples and exercises include traditional analytical ones alongside data-based ones requiring computational approaches.

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