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To determine if the given table represents a probability distribution, we need to check two key conditions:

1. **Non-negativity**: Each probability \( P(x) \) must be greater than or equal to zero.
2. **Total Probability**: The sum of all probabilities must equal 1.

Here is the table provided:

\[
\begin{array}{|c|c|}
\hline
x & P(x) \\
\hline
0 & 0.25 \\
1 & 0.3 \\
2 & 0.25 \\
3 & 5.5511151231258 \times 10^{-17} \\
\hline
\end{array}
\]

Let's check the conditions:

- **Non-negativity**: All the \( P(x) \) values are non-negative. The last probability value, \( 5.5511151231258 \times 10^{-17} \), is a very small positive number (close to zero but still non-negative).
  
- **Total Probability**: The sum of all probabilities is:
  
  \[
  0.25 + 0.3 + 0.25 + 5.5511151231258 \times 10^{-17} = 0.8 + 0.2 \times 10^{-16} \approx 0.8
  \]

Since the sum of the probabilities is not equal to 1, **this is not a valid probability distribution**.

Therefore, the correct answer is:

- No, it is not a probability distribution.

Would you like any further details or clarifications?

Here are 5 related questions to expand your understanding:
1. What are the requirements for a valid probability distribution?
2. How would you correct the given table to make it a valid probability distribution?
3. Why must the sum of probabilities in a distribution always equal 1?
4. Can a probability value be negative? Why or why not?
5. What happens if the sum of probabilities exceeds 1?

**Tip**: When checking for a valid probability distribution, always verify both non-negativity and that the total sum equals 1.

Determine whether this table represents a probability distribution.

Learn how to determine whether a table represents a probability distribution by checking non-negativity and ensuring that the sum of probabilities equals 1. This step-by-step solution walks through the process using a given table.

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