Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.
(a) The number of light bulbs that burn out in the next week in a room with 13 bulbs.
(b) The amount of snowfall.
(a) Is the number of light bulbs that burn out in the next week in a room with 13 bulbs discrete or continuous?
A. The random variable is continuous. The possible values are $x=0,1,2, \ldots, 13$.
B. The random variable is discrete. The possible values are $0 \leq x \leq 13$.
C. The random variable is continuous. The possible values are $0 \leq x \leq 13$.
D. The random variable is discrete. The possible values are $x=0,1,2, \ldots, 13$.
Answer
Final Answer: \(\boxed{\text{D. The random variable is discrete. The possible values are } x=0,1,2, \ldots, 13}\)
Step 1 ：The question is asking whether the random variable, which is the number of light bulbs that burn out in the next week in a room with 13 bulbs, is discrete or continuous. A discrete variable is one that can only take on a finite or countably infinite number of values. A continuous variable is one that can take on any value within a certain range.
Step 2 ：In this case, the number of light bulbs that can burn out is a countable number, ranging from 0 to 13. Therefore, the random variable is discrete. The possible values are \(x=0,1,2, \ldots, 13\).
Step 3 ：Final Answer: \(\boxed{\text{D. The random variable is discrete. The possible values are } x=0,1,2, \ldots, 13}\)
