AP Statistics Curriculum 2007 Fisher F

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General Advance-Placement (AP) Statistics Curriculum - Fisher's F Distribution

Fisher's F Distribution

Commonly used as the null distribution of a test statistic, such as in analysis of variance (ANOVA). Relationship to the t-distribution and [beta Distribution].

PDF:
\frac{\sqrt{\frac{(d_1\,x)^{d_1}\,\,d_2^{d_2}}
{(d_1\,x+d_2)^{d_1+d_2}}}}
{x\,\mathrm{B}\!\left(\frac{d_1}{2},\frac{d_2}{2}\right)}\!

CDF:
I_{\frac{d_1 x}{d_1 x + d_2}}(d_1/2, d_2/2)\!

Mean:
\frac{d_2}{d_2-2}\! for d2 > 2

Median:
None

Variance:
\frac{2\,d_2^2\,(d_1+d_2-2)}{d_1 (d_2-2)^2 (d_2-4)}\! for d2 > 4

Support:
x \in [0, +\infty)\!

1st Moment:


2nd Moment:


Kth Moment:

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