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Chi-Square Distribution
The chi-square distribution with n
degrees of freedom is the continuous probability distribution
with the following probability density function:
The notation
denotes that the random variable X has a chi-square
distribution with n degrees of freedom. The random
variable X is also the sum of the square of n independent
standard normal variables. That is, if Z1 , Z2
, .... Zn is a set of n independent standard
normal variables, then
The sum of two independent random variables that both have
chi-square distributions (but may have different degrees of
freedom) is also a random variable with a chi-square
distribution, whose degree of freedom is the sum of the degrees
of freedom of the two independent random variables. That is, if X
and Y are independent,
The Lower and Upper Percentiles of the Chi-Square Distribution
Tables of any Statistics book tabulates the values of selected
upper and lower percentiles for the chi-square distribution with n
degrees of freedom, where n is an integer from 1 to 30.
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