Statistics Assignment Help With Exact Sampling distributions

11.1 Chi-Square Variate:

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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