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 18 bulbs, (b) The time in minutes required to download a file from the Internet. (a) Is the number of light bulbs that burn out in the next week in a room with 18 bulbs discrete or continuous? A. The random variable is discrete. The possible values are $$ 0 \leq x \leq 18 $$. B. The random variable is continuous. The possible values are $$ x=0,1,2, \ldots, 18 $$, The random variable is continuous. The possible values are $$ 0 \leq x \leq 18 $$, C. The random variable is discrete. The possible, values are $$ x=0,1,2, \ldots, 18 $$. D. Th

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**Step 1. Identify the random variable**  
Let $$ X $$ represent the number of light bulbs that burn out in the next week in a room containing 18 bulbs.

**Step 2. Determine the type (discrete or continuous)**  
Even though the light bulbs may burn out at any moment in time, the random variable $$ X $$ is counting the number of bulbs that burn out. Since the number of items counted is a countable quantity, $$ X $$ is a **discrete** random variable.

**Step 3. Specify the possible values for the random variable**  
Because there are 18 bulbs in the room, no more than 18 bulbs can burn out. Additionally, negative counts are not possible. Therefore, the possible values of $$ X $$ are  
$$
x = 0, 1, 2, \ldots, 18.
$$

**Step 4. Select the correct answer**  
Option C states:  
"The random variable is discrete. The possible values are $$ x=0,1,2, \ldots, 18 $$."

Thus, the correct answer is **C**.
The random variable is discrete, and the possible values are $$ x = 0, 1, 2, \ldots, 18 $$.

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