distribusjonsfunksjon

A distribution function, also known as a cumulative distribution function (CDF), is a fundamental concept in probability theory and statistics. It describes the probability that a random variable takes on a value less than or equal to a given value. The CDF is denoted by F(x) and is defined for all real numbers x.

The domain of the CDF is the set of all real numbers, while the range is the interval [0, 1]. The CDF is non-decreasing, meaning that if x1 < x2, then F(x1) ≤ F(x2). It is also right-continuous, meaning that the limit of F(x) as x approaches a value from the right is equal to F(x).

The CDF can be used to calculate probabilities for a random variable. For example, the probability that a random variable X is less than or equal to a given value x is given by F(x). Similarly, the probability that X is greater than a given value x is given by 1 - F(x).

The CDF is closely related to the probability density function (PDF) and the probability mass function (PMF). For a continuous random variable, the CDF is the integral of the PDF. For a discrete random variable, the CDF is the sum of the PMF.

The CDF is a useful tool in statistical analysis, as it provides a complete description of the distribution of a random variable. It can be used to calculate various statistical measures, such as the mean, median, and mode, and to compare the distributions of different random variables.