To determine whether the given table represents a discrete probability distribution, we need to check two conditions:
- Each probability \( P(x) \) must be between 0 and 1 (inclusive).
- The sum of all probabilities must equal 1.
Given the data:
\[ \begin{array}{|c|c|} \hline x & P(x) \ \hline 56 & 0.3 \ 66 & 0.8 \ 76 & 0.2 \ 86 & -0.3 \ \hline \end{array} \]
Let's check the values of \( P(x) \):
- \( P(56) = 0.3 \): This is between 0 and 1.
- \( P(66) = 0.8 \): This is also between 0 and 1.
- \( P(76) = 0.2 \): This is again between 0 and 1.
- \( P(86) = -0.3 \): This is not between 0 and 1; it is negative.
Now, let's check the sum of the probabilities:
\[ 0.3 + 0.8 + 0.2 - 0.3 = 1.0 \]
The sum of the probabilities is 1, which satisfies one of the conditions.
However, the negative probability \( P(86) = -0.3 \) violates the first condition that each probability must be between 0 and 1.
Conclusion: The table does not represent a discrete probability distribution because one of the probabilities is negative.