Normal distribution意思

"Normal distribution" or "Gaussian distribution" is a type of continuous probability distribution that describes many natural phenomena and is used extensively in statistics and other fields. It is named after its inventor, the mathematician Carl Friedrich Gauss. The normal distribution is particularly useful because it can be used to model a wide variety of phenomena, from the heights of people to the scores on standardized tests.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean is the average value of the distribution, and the standard deviation is a measure of how spread out the data is. The normal distribution is symmetric and bell-shaped, with the highest point at the mean.

The probability density function (PDF) of a normal distribution is given by:

f(x) = (1 / σ√(2π)) * exp(-((x - μ)^2) / (2σ^2))

where x is a value, μ is the mean, σ is the standard deviation, and exp is the base of the natural logarithm (approximately 2.71828).

The normal distribution is important because it is the basis for many statistical tests and methods, such as the z-test and the t-test. It is also used in regression analysis and in the field of machine learning.