To determine whether this table represents a discrete probability distribution, we need to verify that it satisfies two key conditions for probability distributions:

1. Non-negative Probabilities: All values in the probability column, $P(x)$, must be non-negative (i.e., each probability must be greater than or equal to zero).
2. Sum of Probabilities Equals 1: The probabilities of all outcomes must sum up to 1.

Let’s examine each condition for the given table:

Given Table

1. Non-negative Probabilities: The value $P(86) = -0.3$ is negative, which violates the first condition.
2. Sum of Probabilities: If we were to add up the probabilities: $0.3 + 0.3 + 0.2 + (-0.3) = 0.5$ This sum is not equal to 1, which violates the second condition.

Since both conditions are violated, this table does not represent a discrete probability distribution.

Would you like further details or have any other questions about this solution?

Related Questions

1. What are the basic requirements for a probability distribution?
2. How would you adjust the values in this table to make it a valid probability distribution?
3. What distinguishes a discrete probability distribution from a continuous one?
4. Can probabilities ever be negative in any kind of probability model?
5. How do you calculate the mean of a discrete probability distribution?

Tip

When verifying a probability distribution, always check both the sum of probabilities and ensure all probabilities are non-negative.