Probability density function

Probability Density Function

The Probability Density Function (pronounced: prah-buh-bil-i-tee den-si-tee funk-shun), often abbreviated as PDF, is a statistical term that describes the likelihood of a random variable taking on a specific value. The concept is fundamental in the field of Probability Theory and Statistics.

Etymology

The term "Probability Density Function" is derived from the mathematical concepts of probability, density, and function. The term was first used in the early 20th century as statisticians began to formalize the mathematical laws governing random variables.

Definition

In Statistics, a Probability Density Function is a function that describes the likelihood for a Random Variable to take on a given value. The probability for the random variable to fall within a particular region is given by the integral of the variable’s density over the region. The Probability Density Function is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value.

Related Terms

• Cumulative Distribution Function: The function that maps values to their percentile rank in a probability distribution.
• Random Variable: A variable whose possible values are outcomes of a random phenomenon.
• Probability Mass Function: A function that gives the probability that a discrete random variable is exactly equal to some value.
• Expected Value: The long-run average value of repetitions of the experiment it represents.

Applications

Probability Density Functions are used in a wide range of fields, including Physics, Engineering, Computer Science, and Economics. They are particularly useful in Statistical Analysis and Predictive Modeling.

See Also

• Probability Theory
• Statistics
• Random Variable
• Cumulative Distribution Function
• Probability Mass Function
• Expected Value

External links

• Medical encyclopedia article on Probability density function
• Wikipedia's article - Probability density function

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