7. Continuous Random Variables

  1. Paolo Brandimarte

Published Online: 24 MAY 2011

DOI: 10.1002/9781118023525.ch7

Quantitative Methods: An Introduction for Business Management

Quantitative Methods: An Introduction for Business Management

How to Cite

Brandimarte, P. (2011) Continuous Random Variables, in Quantitative Methods: An Introduction for Business Management, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118023525.ch7

Publication History

  1. Published Online: 24 MAY 2011
  2. Published Print: 4 APR 2011

ISBN Information

Print ISBN: 9780470496343

Online ISBN: 9781118023525

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Keywords:

  • continuous random variable;
  • cumulative distribution function;
  • kurtosis;
  • median;
  • mode;
  • probability density function;
  • quantile;
  • skewness;
  • stochastic processes;
  • variance

Summary

This chapter introduces density functions, where the author sees that the concept of cumulative distribution function (CDF) needs no adjustment when moving from discrete to continuous random variables. It explains how expected values and variances are applied in this context. Then, the chapter also talks about the distribution of random variables by considering their mode, median, and quantiles, and describes higher-order moments, skewness, and kurtosis. It also outlines the main theoretical distributions - uniform, beta, triangular, exponential, and normal distributions — and hints at how empirical distributions can be expressed. Further, the chapter explains the sums of independent random variables, and illustrates a few applications, with emphasis on quantiles of the normal distribution. Finally, it considers sequences of random variables in time, i.e., stochastic processes.

Controlled Vocabulary Terms

continuous random variable; cumulative distribution function; kurtosis; median; mode; probability density function; quantile function; skewness; stochastic processes; variance