Question

Determine whether or not the distribution is a probability distribution and select the reason(s) why or why not. Select all that apply.

1) The sum of all probabilities is not equal to 1
2) The probabilities are not non-negative
3) The probabilities are not between 0 and 1
4) The probabilities are not mutually exclusive

Answer 1

The given distribution is not a probability distribution because the sum of all probabilities is not equal to 1 and the probabilities are not non-negative or between 0 and 1.

Step-by-step explanation:

In order to determine whether or not the distribution is a probability distribution, we need to consider the following criteria:

1. The sum of all probabilities must be equal to 1.
2. The probabilities must be non-negative.
3. The probabilities must be between 0 and 1 inclusive.
4. The probabilities must be mutually exclusive.

Based on these criteria, we can select the reasons why the given distribution is not a probability distribution:

1. The sum of all probabilities is not equal to 1. This violates the requirement that the sum of all probabilities must be equal to 1.
2. The probabilities are not non-negative. This violates the requirement that the probabilities must be non-negative.
3. The probabilities are not between 0 and 1. This violates the requirement that the probabilities must be between 0 and 1 inclusive.
4. The probabilities being mutually exclusive is not applicable in this case.