Comparing Discrete and Continuous Random Variables
These practice problems focus on distinguishing discrete versus continuous random variables. Random variables represent quantities or qualities that randomly change within a population. Solve the following problems about discrete and continuous random variables.
Sample questions

Which of the following random variables is discrete?
(A) the length of time a battery lasts
(B) the weight of an adult
(C) the percentage of children in a population who have been vaccinated against measles
(D) the number of books purchased by a student in a year
(E) the distance between a pair of cities
Answer: D. the number of books purchased by a student in a year
A discrete random variable is one that can take on only values that are integers (positive and negative whole numbers and 0). The values of a discrete random variable can have a finite stopping point, like –1, 0, and 1, or they can go to infinity (for example, 1, 2, 3, 4, . . . ).
A continuous random variable takes on all possible values within an interval on the real number line (such as all real numbers between –2 and 2, written as [–2, 2]).
A number of books takes on only positive integer values, such as 0, 1, or 2, and thus is a discrete random variable.

Which of the following random variables isn’t discrete?
(A) the number of children in a family
(B) the annual rainfall in a city
(C) the attendance at a football game
(D) the number of patients treated at an emergency room in a day
(E) the number of classes taken in one semester by a student
Answer: B. the annual rainfall in a city
A discrete random variable is one that can take on only values that are integers (positive and negative whole numbers and 0). The values of a discrete random variable can have a finite stopping point, like –1, 0, and 1, or they can go to infinity (for example, 1, 2, 3, 4, . . . ).
A continuous random variable takes on all possible values within an interval on the real number line (such as all real numbers between –2 and 2, written as [–2, 2]).
The amount of rain that falls on a city in a year can take on any nonnegative value on the real number line, such as 11.45 inches or 37.9 inches, and therefore is continuous rather than discrete.
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