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: \(\boxed{\text{D. The random variable is discrete. The possible values are } x=0,1,2, \ldots, 13}\)