Let be a sum of squares of independent normal standardized variates , and suppose where is a quadratic form in the , distributed as chi-squared with degrees of freedom. Then is distributed as with degrees of freedom and is independent of . The converse of this theorem is known as Cochran's theorem.
Fisher's Theorem
See also
Chi-Squared Distribution, Cochran's TheoremExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Fisher's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FishersTheorem.html