densitetfunksjonen

Densitetfunksjonen, often referred to as the probability density function (PDF) in English, is a fundamental concept in probability theory and statistics. It describes the relative likelihood for a continuous random variable to take on a given value. Unlike probability mass functions for discrete variables, the PDF does not give the probability at a specific point, as the probability of a continuous variable taking on any single exact value is zero. Instead, the area under the curve of the PDF between two points represents the probability that the variable falls within that interval.

The integral of the density function over its entire domain must equal one, signifying that the total probability of the variable taking on some value is 100%. Mathematically, for a continuous random variable X with probability density function f(x), the probability that X lies between values a and b is given by the integral of f(x) from a to b. The density function is always non-negative, meaning f(x) >= 0 for all x. Common examples of distributions defined by density functions include the normal distribution, exponential distribution, and uniform distribution. Understanding the density function is crucial for analyzing and modeling continuous data in various fields.