EXAMPLE 2Identifying discrete and continuous random variables
For the following random variables, (i) determine whether they are discrete or continuous, and (ii) indicate the possible values they can take:
The number of automobiles owned by a family
The width of your desk in this classroom
The number of games played in the next World Series
The weight of model year 2015 SUVs
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Solution
The possible number of automobiles owned by a family is finite and may be written as a list of numbers, so it represents a discrete random variable. The possible values are .
Width is something that must be measured, not counted. Width can take infinitely many different possible values, with these values forming an interval on the number line. Thus, the width of your desk is a continuous random variable. The possible values might be .
The number of games played in the next World Series can be counted and thus represents a discrete random variable. The possible values are finite and may be written as a list of numbers: .
The weight of model year 2015 SUVs must be measured, not counted, and thus represents a continuous random variable. Weight can take infinitely many different possible values, with these values forming an interval on the number line: .