Question

determine whether the following value is a continuous random variable, discrete random variable, or not a random variable.
a. the number of pigeons in a country
b. the \yes\ or
o\ response to a survey question
c. the number of free - throw attempts before the first shot is missed
d. the time it takes for a light bulb to burn out
e. the time required to upload a file to the internet
f. the number of textbook authors now eating a meal
a. is the number of pigeons in a country a discrete random variable, continuous random variable, or not a random variable?
a. it is a continuous random variable.
b. it is a discrete random variable.
c. it is not a random variable.
b. is the \yes\ or
o\ response to a survey question a discrete random variable, continuous random variable, or not a random variable?
a. it is a discrete random variable.
b. it is a continuous random variable.
c. it is not a random variable.
c. is the number of free - throw attempts before the first shot is missed a discrete random variable, continuous random variable, or not a random variable?
a. it is a continuous random variable.

Explanation:

Step1: Recall variable - type definitions

A discrete random variable has a countable number of possible values. A continuous random variable can take on any value in an interval.

Step2: Analyze part a

The number of pigeons in a country is a countable quantity. So it is a discrete random variable.

Step3: Analyze part b

The "yes" or "no" response to a survey question is a categorical variable that can be coded as 0 (no) and 1 (yes). It is a discrete random variable.

Step4: Analyze part c

The number of free - throw attempts before the first shot is missed is a countable number (0, 1, 2, etc.). So it is a discrete random variable.

Step5: Analyze part d

The time it takes for a light bulb to burn out can take on any non - negative real value within an interval. It is a continuous random variable.

Step6: Analyze part e

The time required to upload a file to the Internet can take on any non - negative real value within an interval. It is a continuous random variable.

Step7: Analyze part f

The number of textbook authors now eating a meal is a countable quantity. So it is a discrete random variable.

Answer:

a. B. It is a discrete random variable.
b. A. It is a discrete random variable.
c. B. It is a discrete random variable.
d. A. It is a continuous random variable.
e. A. It is a continuous random variable.
f. B. It is a discrete random variable.