Taylor surveys students in one grade level who own at least one pet. She finds that 50% of the students surveyed own 2 pets, 3 students own 3 pets each, and 2 students own 4 pets each. Eight of the students in the grade own 1 pet. Considering the number of pets as the random variable, X, which of the following is the probability distribution, PX(x)?

To find the probability distribution, PX(x), we need to determine the probability of each possible value of the random variable, X.

From the given information:
- 50% of the students own 2 pets.
- 3 students own 3 pets each.
- 2 students own 4 pets each.
- 8 students own 1 pet.

Let's calculate the probabilities for each value of X:

P(X = 1) = 8 students own 1 pet out of the total surveyed students. So, the probability is 8/total surveyed students.

P(X = 2) = 50% of the students own 2 pets. So, the probability is 50% / total surveyed students.

P(X = 3) = 3 students own 3 pets each. So, the probability is 3 / total surveyed students.

P(X = 4) = 2 students own 4 pets each. So, the probability is 2 / total surveyed students.

The total number of probabilities should sum up to 1, meaning we have accounted for all possibilities.

Therefore, PX(x) is as follows:
- P(X = 1) = 8/total surveyed students
- P(X = 2) = 50% / total surveyed students
- P(X = 3) = 3 / total surveyed students
- P(X = 4) = 2 / total surveyed students

Please note that the exact value of PX(x) depends on the total number of students surveyed, which is not provided in the question.

learn and study mother offer