A page in a book can have at most 300 words. X = Number of misprints on a page.
Then the random variable is

Options

A. not discrete
B. not continuous
C. discrete
D. continuous

Answer

To determine the nature of the random variable \( X \) representing the number of misprints on a page, we will analyze the characteristics of the variable step by step.

### Step-by-Step Solution:

1. **Understanding the Random Variable**:
- We are given that \( X \) is the number of misprints on a page of a book.

2. **Identifying the Type of Variable**:
- A random variable can be classified as either discrete or continuous.
- A **discrete random variable** is one that can take on a countable number of distinct values. For example, the number of misprints can be 0, 1, 2, ..., up to a maximum number.
- A **continuous random variable**, on the other hand, can take on any value within a given interval. This includes fractions and decimals.

3. **Counting Misprints**:
- The number of misprints is a countable quantity. You cannot have a fraction of a misprint; it must be a whole number (0, 1, 2, ...).
- For instance, if there are 3 misprints, you cannot say there are 3.5 misprints. Thus, the values of \( X \) are specific integers.

4. **Conclusion**:
- Since \( X \) can only take specific integer values (0, 1, 2, ..., up to the maximum number of misprints), it is classified as a discrete random variable.
- Therefore, the correct classification of the random variable \( X \) is that it is **discrete**.

5. **Final Answer**:
- The random variable \( X \) is **discrete**.