4

Discrete Random Variables and Some Important Discrete Probability Distributions

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

# Topics Covered:

- 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 describing ...