Chi-square distribution (chi-square distribution):

Defined:
If our random variable is a standard normal distribution (see the Gaussian distribution of previous blogs), then the squared and subordinate distributions of multiple random variables are chi-squared distributions.
X=y12+y22+?+yn2

Among them, Y1,y2,?, yn are to obey the standard normal distribution of random variables, then xx obey Chi-square distribution, it is worth noting that the NN is the number of random variables become chi-square distribution of degrees of freedom.
Probability density function:

Where x≥0, when x≤0, FK (x) = 0. Here γ represents the Gammagamma function.
Usage Environment:
Chi-square distributions are used in statistics for variance estimation and hypothesis testing, and interested students can search for relevant information.

Expectation and variance:
Expect:
E (X) =n
E (X) =n

Variance:
Var (X) =2n
Var (X) =2n
Properties:

This is a good understanding, chi-squared distribution is a and how to add, it must be a chi-squared distribution, but it is noteworthy that variance and expectations will change. Why? Because his variance and expectations are related to degrees of freedom.

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Chi-square distribution (chi-square distribution):