AP Statistics Curriculum 2007 Fisher F

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 \(d_2 > 2\)

Median:
None

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

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

1st Moment:

2nd Moment:

Kth Moment: