Question

Determine whether the table represents a discrete probability distribution. Explain why or why not.
x| 56 66 76 86
P(x)| .3 .8 .2 -0.3

Answer 1

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

1. Each probability \( P(x) \) must be between 0 and 1 (inclusive).
2. 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.