Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP, 2nd Edition

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 ...