# Math Help - showing that a quantile relation holds

1. ## showing that a quantile relation holds

Use the result of F(3,4) = 1/F(4/3) about F distribution to show that the quantile relation f'subscript'(0.95,3,4) = 1/f'subscript'(0.05,4,3).

2. Using upper percentile points....

Which means that $a=P(F_{3,4}>F_{3,4,a})$

we have with a=.95............

$.95=P(F_{3,4}>F_{3,4,.95})$

(Note that $F_{3,4}$ is a rv and $F_{3,4,a}$ is a percentile point.)

Taking the reciprocal inside the probability we have

$.95=P(F_{3,4}>F_{3,4,.95})$

$=P(F^{-1}_{3,4}

$=P(F_{4,3}

(Which follows by the definition of an F, it's a ratio of chi-squares divided by their dfs.)

And note that

$P(F_{4,3} also.

Thus by the continuity of the densities, these percentile points must be equal....

Hence $F^{-1}_{3,4,.95}$ must equal $F_{4,3,.05}$

and this is true for any probability, not just .05.