sannolikhetsdensitetsfunktioner

A probability density function (PDF) is a statistical expression that defines the probability that a random variable falls within a particular range of values. It is a fundamental concept in probability theory and statistics, particularly in the context of continuous random variables. Unlike probability mass functions, which are used for discrete random variables, PDFs are used for continuous random variables.

The PDF of a continuous random variable X, denoted as f(x), satisfies the following properties:

1. The probability that X falls within a certain interval [a, b] is given by the integral of the PDF over that interval: P(a ≤ X ≤ b) = ∫ from a to b f(x) dx.

2. The total area under the PDF curve over the entire range of X is equal to 1, reflecting the fact that the total probability must sum to 1.

3. The value of the PDF at any specific point is not a probability itself, but rather a density. To find the probability of X being exactly equal to a specific value, the PDF must be integrated over an infinitesimally small interval around that value.

PDFs are widely used in various fields, including physics, engineering, economics, and finance, to model and analyze continuous data. Some common examples of PDFs include the normal distribution, the exponential distribution, and the uniform distribution. Each of these distributions has its own unique characteristics and applications, making PDFs an essential tool in statistical analysis.