Question

determine whether the following value is a continuous random variable, discrete random variable, or not a random variable.
a. the number of home runs in a baseball game
b. the usual mode of transportation of people in city a
c. the number of light bulbs that burn out in the next year in a room with 12 bulbs
d. the number of free - throw attempts before the first shot is missed
e. the number of runs scored during a baseball game
f. the number of people with blood type b in a random sample of 15 people
a. is the number of home runs in a baseball game 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.
b. is the usual mode of transportation of people in city a 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.

Explanation:

• a. The number of home - runs in a baseball game is countable (0, 1, 2, etc.), so it is a discrete random variable.
• b. The usual mode of transportation is a non - numerical category (like car, bus, bike), not a numerical value that can be considered as a random variable in the traditional sense of probability theory dealing with numerical values, so it is not a random variable.
• c. The number of light bulbs that burn out is countable (0, 1, 2, …, 12), so it is a discrete random variable.
• d. The number of free - throw attempts before the first miss is countable (1, 2, 3, etc.), so it is a discrete random variable.
• e. The number of runs scored in a baseball game is countable (0, 1, 2, etc.), so it is a discrete random variable.
• f. The number of people with blood type B in a sample of 15 people is countable (0, 1, …, 15), so it is a discrete random variable.

Answer:

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