Question

Which of the following statements about a discrete random variable and its probability distribution are true?

a. Some negative values of P(X) are allowed as long as ∑ P(X) = 1.
b. The values of P(X) increase to a maximum point and then decrease.
c. Values of P(X) must be greater than or equal to zero.
d. Values of the random variable (X) can never be negative

Answer 1

A discrete random variable can only take on specific, countable values and the values of P(X) must be greater than or equal to zero. Values of the random variable X can be negative.

Step-by-step explanation:

A discrete random variable is a random variable that can only take on specific, countable values. The values of a discrete random variable are obtained by counting. For a discrete probability distribution, each probability must be between zero and one, inclusive, and the sum of the probabilities must be equal to one. Therefore, statement c is true: values of P(X) must be greater than or equal to zero. Statement d is false: values of the random variable X can be negative if they are within the defined range of the random variable.