Gaussiansandsynlighedsfordeling

Gaussiansandsynlighedsfordeling, also known as the Gaussian distribution or normal distribution, is a continuous probability distribution that is widely used in statistics and probability theory. It is characterized by its bell-shaped curve and is defined by two parameters: the mean (μ) and the standard deviation (σ). The mean determines the location of the peak of the curve, while the standard deviation controls the width of the curve. The Gaussian distribution is significant because it arises naturally in many contexts, such as the sum of a large number of independent, identically distributed random variables, due to the Central Limit Theorem. It is also used extensively in various fields, including physics, engineering, and finance, for modeling and analyzing data. The probability density function of the Gaussian distribution is given by:

f(x|μ,σ) = (1 / (σ√(2π))) * exp(-(x - μ)² / (2σ²))

where x is a real-valued random variable, μ is the mean, and σ is the standard deviation. The cumulative distribution function (CDF) of the Gaussian distribution is often denoted by Φ and is used to calculate the probability that a random variable falls within a certain range. The Gaussian distribution has several important properties, including symmetry around the mean, and it is the maximum entropy probability distribution for a given mean and variance.