Chi-Square Distribution

The chi-square distribution with n degrees of freedom is the continuous probability distribution with the following probability density function:

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$7nd016$

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The notation

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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 , .... Z_n is a set of n independent standard normal variables, then

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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,

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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.

Subject:

Statistics [1]

Subject X2:

Statistics [1]