Let X₁,X₂,X₃,X₄ be a random sample of size n = 4 from the normal distribution N(0,1). Show that Σ⁴_i=1(X_i − ‾X)² equals

and argue that these three terms are independent, each with a chi-square distribution with 1 degree of freedom.

Transcribed Image Text:

(X₁X₂)² [X3 - (X₁ + X₂)/2]² [X₁-(X₁ + X2 + X3)/3]² +. + 2 3/2 4/3