# Chapter 5Continuous Random Variables and Some Important Continuous Probability Distributions

*The focus of this chapter is a discussion of some important continuous probability distributions*.

## Topics Covered

- Continuous random variables and their probability distributions
- Determination of cumulative distribution functions (c.d.f.'s) from probability density functions (p.d.f.'s)
- Determination of 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, R, 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
- Test of normality
- Some reliability theory 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 variables ...

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