The Probability Density Function is a fundamental concept in statistics that describes the likelihood of a discrete random variable taking on specific values. It is used to model and analyze situations where outcomes are distinct and countable.
For example, consider the roll of a fair six-sided die. The possible outcomes are the integers 1 through 6. The probability density function for this discrete random variable assigns a probability of 1/6 to each outcome, reflecting the equal likelihood of each face appearing.
The probability density function (PDF) for a discrete random variable X can be represented as follows: