Probability Mass Function and Probability Density Function

What are Probability Mass Function and Probability Density Function?

Probability Mass Function:

The first function is known as the probability mass function (PMF). This function returns the probability that a random variable takes a certain value. Because the PMF returns probabilities, any PMF must have two properties.

1. The value returned from a PMF must be non-negative.
2. The sum across all values supporting a random variable must be one.

Probability Density Function:

PDF is a probability that a random variable, say X, will take a value equal to x. The probability density function (PDF) for any values of y and n can be computed using basic probability.

The pdf f(x) has two important properties:

1. f(x)≥ 0f (x)≥0, for all x
2. $ \int_{\infty }^{\infty} $ f(x)dx = 1

Example of Probability Mass Function and Probability Density Function:

The formula of pdf is:
$ f\left ( x \right )= \frac{d}{dx}F\left (x \right ) $

The formula pmf is:

A PMF equation looks like this: P(X = x).
That means “the probability that X takes on some value x”.