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.