Which statement about a PMF is true?

• A. A PMF assigns probabilities to discrete outcomes.
• B. PMF is defined only for discrete variables.
• C. PMF can take negative values.
• D. PMF is the same as a PDF.

Answer: (B)

A PMF is a function that assigns probability mass to each possible value of a discrete random variable. This means you look at the actual values X can take and specify P(X = x) for those values, with all these probabilities nonnegative and summing to 1. The reason the statement about being defined only for discrete variables is true is that, for a continuous variable, the probability of hitting any exact value is zero, so a probability mass function wouldn’t make sense. Instead, we use a probability density function, which describes density and requires integration to obtain probabilities over intervals. In contrast, the probability mass function is the proper tool for discrete outcomes.

It’s also important to note that a PMF does assign probabilities to discrete outcomes, and those probabilities must be nonnegative and sum to 1, but the defining feature that sets PMFs apart from PDFs is their domain—discrete versus continuous. PMFs are not the same as PDFs, and PMFs cannot take negative values.