Tetthetsfunksjoner

Tetthetsfunksjoner, in Norwegian, translates to density functions in English. In the context of probability and statistics, a probability density function (PDF) describes the relative likelihood for a continuous random variable to take on a given value. The value of a PDF at any particular point is not the probability of the random variable taking on that exact value, which is zero for continuous variables. Instead, the integral of the PDF over a given interval represents the probability that the variable falls within that interval.

The PDF is always non-negative, meaning that f(x) >= 0 for all possible values of x. Furthermore, the total area under the curve of a PDF must equal 1, representing the certainty that the random variable will take on some value within its range. Mathematically, this is expressed as the integral of f(x) from negative infinity to positive infinity equaling 1.

Different types of random variables are associated with different forms of density functions. For example, the normal distribution, often called the bell curve, has a specific PDF that is symmetrical and bell-shaped. Other common density functions include the uniform distribution, where all values within a given range are equally likely, and the exponential distribution, which models the time until an event occurs. Understanding density functions is crucial for analyzing continuous data and making predictions based on probabilistic models.