6.1 Introduction: Continuous Random Variables

The image shows radish plants of various heights sprouting out of dirt.
The heights of these radish plants are continuous random variables. (Credit: Rev Stan)

Learning Objectives

By the end of this chapter, the student should be able to:

  • Recognize and understand continuous probability density functions.
  • Understand that continuous probability distributions are smooth curves or functions in which the area under the curve represents probability.
  • Recognize  and apply the uniform probability distribution.
  • Recognize and apply the exponential probability distribution.
  • Recognize and apply the normal probability distribution.
  • Recognize and apply the standard normal probability distribution.
  • Compare normal probabilities by converting to the standard normal distribution.

Future engineers and scientists may encounter examples such as the velocity of particles in fluid dynamics, the temperature distribution in a material under thermal analysis, or the electrical conductivity across a semiconductor. Additionally, they may explore the distribution of wind speeds in meteorology, the lifespan of electronic components, or the distance traveled by a vehicle between failures in reliability engineering.  The field of reliability depends on a variety of continuous random variables. These examples demonstrate the diverse applications of continuous random variables, highlighting their significance in understanding and predicting real-world phenomena.

Random Variables – Counted or Measured?

The values of discrete and continuous random variables can be ambiguous. For example, if X is equal to the number of miles (to the nearest mile) you drive to work, then X is a discrete random variable. You count the miles. If X is the distance you drive to work, then you measure values of X and X is a continuous random variable. For a second example, if X is equal to the number of books in a backpack, then X is a discrete random variable. If X is the weight of a book, then X is a continuous random variable because weights are measured. How the random variable is defined is very important.

So as a “rule of thumb,” if a random variable is counted, then we regard the variable as discrete.  If the random variable is measured, then we regard the variable as continuous.

 

License

Icon for the Creative Commons Attribution 4.0 International License

Introduction to Statistics for Engineers Copyright © by Vikki Maurer & Jeff Crabill & Linn-Benton Community College is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

Feedback/Errata

Comments are closed.