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# 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

Scientists and engineers often build models for the phenomena they are studying to make predictions and decisions. For example, where and when is this hurricane going to hit when it makes landfall? How many accidents 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, according 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.

In math ...

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