Discrete and continuous models

A discrete probability mass function p(x)=P(X=x) is nonnegative and sums to 1. For a continuous variable with density f, probabilities are areas and P(X=x)=0 at every particular point. A density value is not itself a probability. Discrete models commonly count events; continuous models commonly measure amounts. Rounding may make recorded measurements discrete even when an underlying continuous model is useful.