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 $$ 0 \leq x \leq 18 $$. The random variable is discrete. The possible, values are $$ x=0,1,2, \ldots, 18 $$. D. A. The random variable is continuous. The possible values are $$ t=1,2,3, \ldots $$. B. The random variable is discrete. The possible values are $$ t=1,2,3, \ldots \ldots $$ (b) the in minutes required to download a file from the internet discrete or continuous? C. The random variable is continuous. The possible values are $$ t0 $$, D. The random variable is discrete. The possible values are $$ t0 $$,

Question

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 $$ 0 \leq x \leq 18 $$. The random variable is discrete. The possible, values are $$ x=0,1,2, \ldots, 18 $$. D. A. The random variable is continuous. The possible values are $$ t=1,2,3, \ldots $$. B. The random variable is discrete. The possible values are $$ t=1,2,3, \ldots \ldots $$ (b) the in minutes required to download a file from the internet discrete or continuous? C. The random variable is continuous. The possible values are $$ t>0 $$, D. The random variable is discrete. The possible values are $$ t>0 $$,

UpStudy AI · Accepted Answer

Let's analyze each part of the problem step by step.

### Part (a): The number of light bulbs that burn out in the next week in a room with 18 bulbs.

1. **Type of Random Variable**: 
   - The number of light bulbs that burn out is a countable quantity. You can have 0, 1, 2, ..., up to 18 bulbs that burn out. 
   - Since this variable can only take specific integer values (whole numbers), it is classified as a **discrete random variable**.

2. **Possible Values**: 
   - The possible values of this random variable are $$ x = 0, 1, 2, \ldots, 18 $$.

### Conclusion for Part (a):
- The correct answer is: **The random variable is discrete. The possible values are $$ x = 0, 1, 2, \ldots, 18 $$**.

### Part (b): The time in minutes required to download a file from the Internet.

1. **Type of Random Variable**: 
   - The time taken to download a file can take any value within a range, including fractions of a minute (e.g., 1.5 minutes, 2.3 minutes, etc.). 
   - Since this variable can take any value within a continuous range, it is classified as a **continuous random variable**.

2. **Possible Values**: 
   - The possible values of this random variable are $$ t > 0 $$ (since time cannot be negative).

### Conclusion for Part (b):
- The correct answer is: **The random variable is continuous. The possible values are $$ t > 0 $$**.

### Summary:
- For part (a), the random variable is discrete with possible values $$ x = 0, 1, 2, \ldots, 18 $$.
- For part (b), the random variable is continuous with possible values $$ t > 0 $$.
- **Part (a)**: The number of light bulbs that burn out is **discrete**, with possible values $$ x = 0, 1, 2, \ldots, 18 $$. - **Part (b)**: The time required to download a file is **continuous**, with possible values $$ t > 0 $$.

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