# Chapter 5

# Continuous Random Variables and Some Important Continuous Probability Distributions

**The focus of this chapter is a discussion of some important continuous probability distributions. The topics covered are**:

- Continuous random variables and their probability distributions
- Determination of the cumulative distribution functions from probability density functions
- Determination of the cumulative probabilities for different probability distributions
- Determination of the mean and variance of different continuous probability distributions, including the normal, exponential, gamma, and Weibull distributions
- Determination of the cumulative probabilities for different probability distributions using the statistical packages MINITAB, Microsoft Excel, and JMP
- Approximation of the binomial and Poisson distributions by the normal distribution
- Determination of the mean and the variance of linear functions of independent normal random variables
- Tests of normality
- Some reliability theory and related probability models: lognormal, exponential, gamma, and Weibull distribution

**Learning Outcomes**

After studying this chapter, the reader will be able to

- Understand the difference between discrete and continuous random variables.
- Understand various important continuous distributions and apply them to determine probabilities in real-world problems.
- Determine approximate probabilities of discrete random variables using the normal distribution.
- Determine the mean and the variance of continuous random ...

Get *Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition* now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.