Let the chi square variables \(\chi_{1}^{2}\), with \(v_{1}\) degrees of freedom, and \(\chi_{2}^{2}\), with \(v_{2}\) degrees of freedom, be independent. Establish the result on page 211, that their sum is a chi square variable with \(v_{1}+v_{2}\) degrees of freedom.

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Representation of chi square random variable Let Z1, Z2,..., Zy be independent standard normal random variables. = sum of squares of v independent standard normal variables = Zhas a chi square distribution with v degrees of freedom.