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 σ 2, it is recorded as N(μ, σ 2). 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.
Extended data:
Normal distribution has a very wide practical background, and the probability distribution of many random variables in production and scientific experiments can be approximately described by normal distribution. For example, in the case of unchanged production conditions, the strength, compressive strength, caliber, length and other indicators of the product; Body length, weight and other indicators of the same organism; Weight of the same seed; Measuring the error of the same object; Deviation of the impact point in a certain direction; Annual precipitation in a certain area; And the velocity component of ideal gas molecules, and so on.
Generally speaking, if a quantity is the result of many tiny independent random factors, then it can be considered to have a normal distribution (see the central limit theorem). Theoretically, normal distribution has many good properties, and many probability distributions can be approximated by it. There are also some commonly used probability distributions directly derived from it, such as lognormal distribution, T distribution, F distribution and so on.
Baidu Encyclopedia-Normal Distribution