What is the difference between PDF and PMF?

PDF stands for Probability Density Function, while PMF stands for Probability Mass Function. PMF is basically used when the solution one needs to come up with would have its range within numbers of discrete random variables. While PDF, on the other hand, is basically used when one needs to come up with a range of continuous random variables.

PMF usually uses discrete random variables, while PDF basically uses continuous random variables. PDF is the derivative of CDF, which stands for the cumulative distribution function. The CDF can be used to determine probability whereby a continuous random variable occurs within a measurable subset of a certain range.

In short, the disparity is more on association with continuous rather than the discrete random variables. A continuous random variable is explained as a random variable that actually does cover infinite values. The term continuous do applies to random variables since it can assume all possible values within a given range of probability.

PDF or Probability Density Function and PMF or Probability Mass Function are terms you would definitely come across in advanced physics, math, and calculus. Both are probability measures that are used to determine the possible values for a random variable. When the variable in question is a discrete random variable, probability mass function is used to get the possible values for it.

On the other hand, if the variables in question are continuous random variables, probability density function is used. PDF is usually considered as a type of cumulative distribution function (CDF) because CDF can also be used to determine the possible values for continuous random variables.

Just so you understand what I meant when I used discrete and continuous random variables, think of discrete random variables as countable numbers like 0, 1, 2 3,........9. In contrast, continuous random variables are also countable numbers but also extend to infinite values.