CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 4. Discrete Probability Distribution

CHAPTER

4 Discrete Probability Distribution

Chapter Outline

4.1 TWOTYPES OFRANDOMVARIABLES

4.2 PROBABILITYDISTRIBUTION FOR ADISCRETERANDOMVARIABLE

4.3 MEAN ANDSTANDARDDEVIATION OFDISCRETERANDOMVARIABLES

4.4 THEBINOMIALPROBABILITYDISTRIBUTION

4.5 THEPOISSONPROBABILITYDISTRIBUTION

4.6 THEGEOMETRICPROBABILITYDISTRIBUTION

Introduction

InAn Introduction to Probabilitywe illustrated how probability can be used to make an inference about a population
from a set of data that is observed from an experiment. Most of these experiments were simple events that were
described in words and denoted by capital letters. However, in real life, most of our observations are in the form
of numerical data. These data are observed values of what we call random variables. In this chapter, we will study
random variables and learn how to find probabilities of specific numerical outcomes.

Recall that we defined an experiment as a process in which a measurement is obtained. For example, counting the
number of cars in a parking lot, measuring the average daily rainfall in inches, counting the number of defective
tires in a production line, or measuring the weight in kilograms of an African elephant cub. All these are called
quantitative variables.

If we letxrepresent a quantitative variable that can be measured or observed in an experiment, then we will be
interested in finding the numerical value of this quantitative variable. For example,x=the weight in kg of an
African elephant cub. If, however, the quantitative variablextakes a random outcome, we refer to it as arandom
variable.

Definition

Arandom variablerepresents the numerical value of a simple event of an experiment.

Example:

Three voters are asked whether they are in favor of building a charter school in a certain district. Each voter’s
response is recorded as Yes (Y) or No (N). What are the random variables that could be of interest in this experiment?

Solution:

As you may notice, the simple events in this experiment are not numerical in nature, since each outcome is either
a Yes or a No. However, one random variable of interest is thenumberof voters who are in favor of building the
school.

The table below shows all thepossible outcomes from a sample of three voters. Notice that we assigned 3 to the first
simple event (3 yes votes), 2 (2 yes votes) to the second, 1 to the third (1 yes vote), and 0 to the fourth (0 yes votes).