Page 147 - Statistics for Dummies

Chapter 8
Random Variables and the
Binomial Distribution
In This Chapter
▶ Identifying a binomial random variable
▶ Finding probabilities using a formula or table
▶ Calculating the mean and variance
cientists and engineers often build models for the phenomena they are
Sstudying to make predictions and decisions. For example, where and
when is this hurricane going to hit when it makes landfall? How many acci-
dents will occur at this intersection this year if it’s not redone? Or, what will
the deer population be like in a certain region five years from now?
To answer these questions, scientists (usually working with statisticians)
define a characteristic they are measuring or counting (such as number of
intersections, location and time when a hurricane hits, population size, and
so on) and treat it as a variable that changes in some random way, accord-
ing to a certain pattern. They cleverly call them — you guessed it — random
variables. In this chapter, you find out more about random variables, their
types and characteristics, and why they are important. And you look at the
details of one of the most common random variables: the binomial.

Defining a Random Variable

A random variable is a characteristic, measurement, or count that changes
randomly according to a certain set or pattern. Its notation is X, Y, Z, and so
on. In this section, you see how different random variables are characterized
and how they behave in the long term in terms of their means and standard
deviations.

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