What is the Difference Between Probability Distribution Function and Probability Density Function?

The main difference between a probability distribution function and a probability density function lies in the type of random variables they represent.

• Probability Distribution Function (PDF): This function represents a discrete probability distribution, where the random variable takes values that differ by fixed amounts and are separated by gaps containing no values. In this case, the output of a probability mass function is a probability.
• Probability Density Function (PDF): This function represents a continuous probability distribution, where the random variable takes values that differ by arbitrarily small amounts and are separated by gaps containing no values. The area under the curve produced by a probability density function represents the probability of an outcome falling within a specific range.

In summary:

• Probability Distribution Function is used for discrete random variables.
• Probability Density Function is used for continuous random variables.

Both probability distribution functions and probability density functions are used to represent the likelihood of an event happening and are commonly referred to as probability distributions.

Comparative Table: Probability Distribution Function vs Probability Density Function

The main difference between a Probability Distribution Function and a Probability Density Function lies in the nature of the random variables they describe. Here is a table summarizing the differences:

In summary, a Probability Distribution Function is used to describe the probability of a continuous random variable taking a value less than or equal to a given value, while a Probability Density Function is used to describe the probability of a discrete random variable taking a specific value.