Question

Which of the following are valid probability distributions for a discrete random variable? Check all that apply.

a. 1/12, 1/12, 1/12, 1/12.5

b. 5, 5.5, 5.5, 5.5

c. 1/6, 5/4, 3/2, 7/8

d. 1/16, 1/32, 1/64, 1/128, 1/128

Answer 1

Only option (d) represents a valid probability distribution for a discrete random variable, as it is the only option where each probability is between zero and one, and the sum of all probabilities equals one.

Step-by-step explanation:

The question concerns the identification of valid probability distributions for a discrete random variable. To be a valid probability distribution:

1. Each probability must be between zero and one, inclusive.
2. The sum of all probabilities must equal one.

Let's evaluate the given options:

• a. This is not valid because the probabilities do not sum up to one.
• b. This is not valid because the values are greater than one and do not sum up to one.
• c. This is not valid because although the total exceeds one, individual probabilities are not all between zero and one inclusive.
• d. This is valid as all probabilities are between zero and one, and they sum up to one.

Therefore, only option (d) is a valid discrete probability distribution