Which statement best differentiates a PMF from a PDF?

Which statement best differentiates a PMF from a PDF?

• A. PMF assigns probabilities to discrete outcomes.
• B. PMF describes continuous densities with infinite support.
• C. PMF integrates to 1 over the range of X.
• D. PMF is the same as a PDF.

Answer: (A)

PMF is a function that assigns probabilities to discrete outcomes of a random variable. Since the variable can take only specific values, each outcome has a probability P(X = x), and all these probabilities add up to 1. This contrasts with a PDF, which applies to continuous variables where a single point has zero probability; instead, probabilities come from integrating the density over an interval. That’s why the statement capturing the distinction is that a PMF assigns probabilities to discrete outcomes. The other options don’t fit: a PMF does not describe continuous densities, it does not use integration to total 1 (it uses summation to 1), and it is not the same as a PDF.

PMF is a function that assigns probabilities to discrete outcomes of a random variable. Since the variable can take only specific values, each outcome has a probability P(X = x), and all these probabilities add up to 1. This contrasts with a PDF, which applies to continuous variables where a single point has zero probability; instead, probabilities come from integrating the density over an interval.

That’s why the statement capturing the distinction is that a PMF assigns probabilities to discrete outcomes. The other options don’t fit: a PMF does not describe continuous densities, it does not use integration to total 1 (it uses summation to 1), and it is not the same as a PDF.