In the following probability distribution, the random variable $x$ represents the number of activities a parent of a 6 th- to 8th-grade student is involved in. Complete parts (a) through (f) below.
\begin{tabular}{c|c|c|c|c|c}
$\mathbf{x}$ & 0 & 1 & 2 & 3 & 4 \\
\hline $\mathbf{P}(\mathbf{x})$ & 0.318 & 0.294 & 0.126 & 0.072 & 0.190
\end{tabular}
(a) Verify that this is a discrete probability distribution.
This is a discrete probability distribution because the sum of the probabilities is and each probability is
greater than or equal to 0 .
between 0 and 1 , inclusive.
greater than 0 and less than 1.
less than or equal to 1 .

Step 1 ：Given the probability distribution of the random variable $x$ which represents the number of activities a parent of a 6th- to 8th-grade student is involved in, we need to verify that this is a discrete probability distribution.

Step 2 ：To verify that this is a discrete probability distribution, we need to check two conditions: 1. Each probability is between 0 and 1, inclusive. 2. The sum of all probabilities is 1.

Step 3 ：The given probabilities are 0.318, 0.294, 0.126, 0.072, and 0.190.

Step 4 ：Checking the first condition, we can see that all the given probabilities are between 0 and 1, inclusive.

Step 5 ：Checking the second condition, we need to sum up all the probabilities and check if the sum is equal to 1.

Step 6 ：The sum of all probabilities is 0.318 + 0.294 + 0.126 + 0.072 + 0.190 = 1.0

Step 7 ：Since the sum of all probabilities is 1, the second condition is also satisfied.

Step 8 ：Since both conditions are satisfied, we can conclude that the given distribution is a discrete probability distribution.

Step 9 ：\(\boxed{\text{Yes}}\), the given distribution is a discrete probability distribution because all the probabilities are between 0 and 1, inclusive, and the sum of all probabilities is 1.