Probability mass function ($p_X(x)$)

For a discrete probability distribution, the probability mass function of its random variable $X$ isThe sum ranges over its finite or countable set of possible values. An event's probability is the sum of the masses of the included values. For the example under probability distribution, $\mathbb{P}(X\ge 1)=p_X(1)+p_X(3)=0.8$. The cumulative distribution function sums masses below a threshold; its jump at a value equals that value's probability mass. This differs from a probability density function, whose height is not a point probability.

A probability mass function obtained by summing a joint probability mass function over the unretained coordinates. Nonnegative summands ensure that iterated sums are well defined.