Question

determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
a. the number of free - throw attempts before the first shot is made
b. the number of bald eagles in a country
c. the response to the survey question \did you smoke in the last week?\
d. the number of points scored during a basketball game
e. the distance a baseball travels in the air after being hit
f. the number of textbook authors now sitting at a computer
a. is the number of free - throw attempts before the first shot is made a discrete random variable, a 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.

Explanation:

• Discrete random variable: A discrete random variable has a countable number of possible values. For example, the number of free - throw attempts before the first shot is made (a) is a non - negative integer (0, 1, 2,...), the number of bald eagles in a country (b) is a non - negative integer, the number of points scored during a basketball game (d) is a non - negative integer, and the number of textbook authors now sitting at a computer (f) is a non - negative integer. These are all countable values.
• Not a random variable: A random variable is a variable whose value is determined by the outcome of a random event. The response to the survey question “Did you smoke in the last week?” (c) is a categorical variable (yes/no), not a numerical variable that can be considered a random variable in the traditional sense of having numerical values that result from a random process with a probability distribution. The distance a baseball travels in the air after being hit (e) is a continuous random variable as it can take on any value within a certain range (e.g., 100.5 feet, 200.34 feet etc.).

Answer:

a. B. It is a discrete random variable.
b. B. It is a discrete random variable.
c. C. It is not a random variable.
d. B. It is a discrete random variable.
e. A. It is a continuous random variable.
f. B. It is a discrete random variable.