Tihedusjaotus

Tihedusjaotus, also known as probability density function (PDF) in English, is a fundamental concept in probability theory and statistics. It describes the likelihood of a continuous random variable taking on a particular value. Unlike discrete random variables, which have a probability mass function (PMF), continuous random variables have a PDF that represents the density of probability over a range of values.

The PDF is defined such that the probability of a random variable falling within a particular interval is given by the integral of the PDF over that interval. This means that the total area under the PDF curve must equal 1, as it represents the entire probability distribution. The value of the PDF at any given point is not a probability itself but rather a density, which can be greater than 1.

Common examples of PDFs include the normal distribution, the exponential distribution, and the uniform distribution. Each of these distributions has its own unique shape and characteristics, but they all share the property that their integral over the entire range of the random variable equals 1.

Tihedusjaotus is crucial in various fields, including physics, engineering, economics, and machine learning. It provides a way to model and analyze continuous data, making it an essential tool for understanding and predicting real-world phenomena. By understanding the PDF of a random variable, one can make informed decisions based on the likelihood of different outcomes.