Normal distribution, also known as "normal distribution" and Gaussian distribution, was first obtained by de moivre in the asymptotic formula for finding binomial distribution. C.F. Gauss deduced it from another angle when studying the measurement error.
Laplace and Gauss studied its properties. It is a very important probability distribution in mathematics, physics, engineering and other fields, and has great influence in many aspects of statistics. The normal curve is bell-shaped, with low ends and high middle, which is symmetrical left and right, so people often call it bell-shaped curve.
If the random variable X obeys the normal distribution with a mathematical expectation of μ and a variance of σ2, it is recorded as N(μ, σ2). The expected value μ of probability density function with normal distribution determines its position, and its standard deviation σ determines its distribution amplitude. When μ=0 and σ= 1, the normal distribution is standard normal distribution.
The concept of normal distribution was first put forward by French mathematician De Moivre in 1733, and was first applied to astronomy by German mathematician Gauss. So the normal distribution is also called Gaussian distribution. Gauss's work had a great influence on later generations. At the same time, he named it Gaussian distribution, and later generations attributed the invention right of the least square method to him.
Graphic features:
1, concentration: the peak of the normal curve is located in the center, that is, where the average value is located.
2. Symmetry: The normal curve is centered on the mean value, which is symmetrical left and right, and both ends of the curve never intersect with the horizontal axis.
3. Uniform variation: the normal curve starts from the place where the mean value is located and gradually decreases evenly to the left and right sides respectively.