Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition

Chapter 4

Discrete Random Variables and Some Important Discrete Probability Distributions

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

• Discrete random variables and some important probability distributions
• Approximation of the binomial by the Poisson distribution
• Determination of the cumulative distribution functions (c.d.f.) from probability functions
• Determination of the mean and variance of different discrete random variables.
• Determination of the probabilities of events involving discrete random variables using the statistical packages MINITAB, Microsoft Excel, and JMP

Learning Outcomes

After studying this chapter, the reader will be able to

• Understand various important discrete distributions and apply them to determine probabilities in real-world problems.
• Determine approximate probabilities of rare events.
• Determine the mean and the variance of discrete random variables using general techniques and moment-generating functions.
• Apply the statistical packages MINITAB, Microsoft Excel, and JMP to calculate probabilities when using different discrete probability models.

4.1 Graphical Descriptions of Discrete Distributions

In Chapter 2 we discussed methods of describing empirical distributions, that is, distributions of the numerical values of the measurements obtained in a sample. In Chapter 3 we discussed basic concepts of probability theory. In this chapter we discuss methods that can be used for ...