Question

determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
a. the amount of rain in city b during april
b. the number of light bulbs that burn out in the next week in a room with 10 bulbs
c. the eye color of people on commercial aircraft flights
d. the time it takes for a light bulb to burn out
e. the number of textbook authors now sitting at a computer
f. the time required to download a file from the internet

Explanation:

• a. The amount of rain in City B during April: Rainfall can take any value within a range (e.g., 1.5 inches, 2.34 inches), so it is a continuous random variable.
• b. The number of light bulbs that burn out in the next week in a room with 10 bulbs: The number of bulbs that burn out can be 0, 1, 2,..., 10. These are distinct, countable values, so it is a discrete random variable.
• c. The eye color of people on commercial aircraft flights: Eye - color is a categorical variable (e.g., blue, brown, green). It is not a numerical variable that can be measured on a continuous or discrete numerical scale, so it is not a random variable.
• d. The time it takes for a light bulb to burn out: Time can take any value within a range (e.g., 100.5 hours, 200.34 hours), so it is a continuous random variable.
• e. The number of textbook authors now sitting at a computer: The number of authors can be 0, 1, 2,..., which are distinct, countable values, so it is a discrete random variable.
• f. The time required to download a file from the Internet: Time can take any value within a range (e.g., 10.5 seconds, 20.34 seconds), so it is a continuous random variable.

Answer:

a. Continuous random variable.
b. Discrete random variable.
c. Not a random variable.
d. Continuous random variable.
e. Discrete random variable.
f. Continuous random variable.