Question

The following probability distribution, the random variable x represents the number of activities a parent of a 5th-grade student is involved in arts. (a) Verify that this is a discrete probability distribution. (b) What is the sum of the probabilities? (c) What is the value of each probability?

Answer 1

This is a discrete probability distribution with probabilities ranging from 0 to 1, with a sum of 1. The probabilities for each value of x are 0.6, 0.6, 1, 0.6, 0.22, and 0.04.

Step-by-step explanation:

In order to verify that this is a discrete probability distribution, we need to check that:

1. The values of the random variable are finite and countable. In this case, the values of x are 0, 1, 2, 3, 4, and 5, which are indeed finite and countable.
2. Each probability, P(x), is between 0 and 1, inclusive. In the given table, all probabilities are between 0 and 1.
3. The sum of all probabilities is 1. In this case, the sum of all probabilities is indeed 1. (30/50) + (30/50) + (50/50) + (30/50) + (11/50) + (2/50) = 1.

The sum of the probabilities is 1, and each probability is between 0 and 1, so this is indeed a discrete probability distribution.

The value of each probability can be obtained from the given table:

• P(0) = 30/50 = 0.6
• P(1) = 30/50 = 0.6
• P(2) = 50/50 = 1
• P(3) = 30/50 = 0.6
• P(4) = 11/50 = 0.22
• P(5) = 2/50 = 0.04