The Gaussian distribution, or normal distribution, is one of the most common probability distributions in statistics. It is used to model various phenomena such as human height, air temperature, measurement errors, and many others.
A normal distribution is described by two parameters: mathematical expectation (μ) and standard deviation (σ). The mathematical expectation determines the center of the distribution, and the standard deviation determines its spread.
Graphically, the normal distribution is represented as a bell-shaped curve, symmetrical with respect to the mathematical expectation. This curve has a peculiarity - most values are concentrated around the mathematical expectation, and values located at a certain distance from it become less and less likely.
The normal distribution is the basis for many statistical methods and models, such as t-tests, analysis of variance, and linear regression. It is also widely used in physics, economics, engineering and other fields of science.
An important feature of the normal distribution is its significance. This means that many random phenomena that occur in the real world can be described using a normal distribution. Moreover, many statistical methods and models operate on the assumption of normality of data.
Despite its popularity, the normal distribution is not universal and is not always the best choice for data modeling. For example, the normal distribution is not suitable for modeling data that is highly skewed or has heavy tails.
In summary, the Gaussian distribution, or normal distribution, is one of the most important and widely used probability distributions in statistics and other fields of science. Its significance lies in the fact that it is the basis for many statistical methods and models, and can also be used to model various random phenomena in the real world.