A probability distribution function (PDF) is a mathematical function that describes the likelihood of various outcomes or events in a random experiment or process. In simple terms, all possible values a random variable can take.

There are two types of Probability distributions :

Discrete Probability Distribution: This type of distribution is used
when the random variable can take on a countable number of distinct values.

Example: Modeling Website Traffic

Imagine you run a website, and you want to model the number of visitors you receive in a given hour. This can be modelled using a discrete probability distribution, such as the Poisson distribution.

Continuous Probability Distribution: Continuous distributions are used
when the random variable can take on any value within a certain range.
Examples of continuous probability distributions include the normal distribution, exponential distribution.,

Example: Modeling Arrival Times of Buses

Consider a public bus system where you want to model the time between bus arrivals at a particular bus stop. This can be approximated by a continuous probability distribution, such as the exponential distribution.

In summary, Probability Distribution Functions are powerful tools for understanding and analyzing randomness in various real-world scenarios. Whether you’re predicting the number of customers in a store, waiting times for a bus, or the heights of individuals in a population, PDFs help quantify uncertainty and make informed decisions.