2. Little Calculus for F-distribution familiarity: Prove Theorem 8.7 by followingthe steps below (our textbook left this for the reader as a small exercise)• Write down formula for 1 − α =R ∞f1−αf(v1,...

2. Little Calculus for F-distribution familiarity: Prove Theorem 8.7 by following
the steps below (our textbook left this for the reader as a small exercise)
• Write down formula for 1 − α =
R ∞
f1−α
f(v1, v2)df and omit the 3 constant
Γ terms since they are symmetric in (v1, v2)
• Set g = 1/f and transform to dependence on g and remember that df =
−dg/g2
.
• Simplify the integrand and note that 1 − α =
R 1/f1−α
0 f(v2, v1)df (note g is
a dummy variable so we’ve replaced it with f in our last statement)
• Show that from the definition for fα we can write 1 − α =
R fα
0
f(v1, v2)df
• Equate the two results for 1 − α and you are done