The square of a standard normal variate is known as chi-square variate with 1 degree of freedom
Thus if X≈ N(μ, σ2), then
And is a chi-square variate with 1 degree of freedom.
In general, if Xi, (i = 1, 2, ……, n) are n independent normal variates with mean μi and variance σi2, (i = 1, 2, ……, n), then
is a chi-square variate with n degrees of freedom.
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