# Difference between pmf and pdf

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pmf = Probability Mass Function
pdf  = Probability Density Function
In probability theory and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.[1] The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.
On the other hand,
a probability density function (PDF), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value. The probability of the random variable falling within a particular range of values is given by the integral of this variable’s density over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range.

A probability mass function differs from a probability density function (pdf) in that the latter is associated with continuous rather than discrete random variables; the values of the latter are not probabilities as such: a pdf must be integrated over an interval to yield a probability.

In summary,
*the PMF is used when the solution that you need to come up with would range within numbers of discrete random variables. PDF, on the other hand, is used when you need to come up with a range of continuous random variables.
* PMF uses discrete random variables.
PDF uses continuous random variables.
Based on studies, PDF is the derivative of CDF, which is the cumulative distribution function. CDF is used to determine the probability wherein a continuous random variable would occur within any measurable subset of a certain range.

Source:
1. Wikipedia
2. difference between