Probability density/mass function I am a bit confused as to the difference between the probability mass function and the probability density function for a distribution of discrete variables. I understand there would be no mass function for a continuous variable distribution, only a density function. But for discrete variable distributions, are there both mass and density functions or are my notes wrong and there is only a mass function?
 A: The difference is in how they are evaluated. They are not quite the same thing.
In a discrete distribution, you have a finite number of events, and each event occurs with some probability. Therefore, since the set of events $E$ is finite, it makes sense to have a function $p$ that maps the events to their probabilities, $p(E) : E \to [0,1]$.
In a continuous distribution, any event occurs with probability zero. So it doesn't make sense to have a function that, when evaluated, returns the probability of the variable being that value. In other words, for a continuous random variable $X$, $P(X = x) = 0$.
What does make sense, however, is a function such that the area underneath it is the probability that the random variable is less than or equal to that value. This is a probability density function. The pdf is so named because it gives you a shape that mimics the density of the distribution of a variable in some domain.
In both cases, the analog to area under the curve from the left gives the probability that the random variable is less than or equal to some value. In the discrete case, this is summation of all values to the left. In the continuous case, it is the area under the curve.
A: I've never liked naming the functions differently for both the discrete and continuous cases. I've always learned them both as "probability density function" (in both the discrete and continuous cases). The probability mass function refers to discrete random variables. 
