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questions :Introduction of normal distribution
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[Member (365WT)]answers [Chinese ]Time :2019-04-23
Normal distribution: is a probability distribution. The normal distribution is a distribution of continuous random variables with two parameters μ and σ^2, the first parameter μ is the mean of the random variables following the normal distribution, and the second parameter σ^2 is the variance of the random variable. Therefore, the normal distribution is denoted as N(μ, σ^2). The probability law of random variables following normal distribution is that the probability of taking the value of μ neighbor is large, and the probability of taking the value farther away from μ is smaller; the smaller the σ is, the more concentrated the distribution is near μ, the larger the σ is, the more the distribution is. dispersion.
The density function of a normal distribution is characterized by a maximum value at μ for μ symmetry, a value of 0 at positive (negative) infinity, and an inflection point at μ ± σ. Its shape is low on both sides of the middle and the image is a bell curve above the x-axis. When μ=0, σ^2 =1, it is called the standard normal distribution and is denoted as N(0,1).

When a μ-dimensional random vector has a similar probability law, the random vector is said to follow a multi-dimensional normal distribution. The multivariate normal distribution has good properties. For example, the edge distribution of the multivariate normal distribution is still a normal distribution, and the random vector obtained by any linear transformation is still a multidimensional normal distribution, especially its linear combination is a unitary normal. distributed.


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