# TI-BASIC:Fpdf

Command Summary

Evaluates the F-distribution probability density function at a point.

Command Syntax

Fpdf(x, numerator df, denominator df)

Press:

1. 2ND DISTR to access the distribution menu
2. 8 to select Fpdf(, or use arrows.

Press 9 instead of 8 on a TI-84+/SE with OS 2.30 or higher.

TI-83/84/+/SE

2 bytes

Fpdf( is the F-distribution probability density function.

Since the F-distribution is continuous, the value of Fpdf( doesn't represent an actual probability - in fact, one of the only uses for this command is to draw a graph of the distribution. You could also use it for various calculus purposes, such as finding inflection points.

The command takes 3 arguments: x is the point at which to evaluate the function (when graphing, use X for this argument), numerator df and denominator df are the numerator degrees of freedom and denominator degrees of freedom respectively (these specify a single Fpdf( curve out of an infinite family).

The F-distribution is used mainly in significance tests of variance.

# Formulas

The value of the Fpdf( is given by

${\displaystyle \definecolor {darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor {darkgreen}\operatorname {Fpdf} (x,d_{1},d_{2})={\frac {\left({\frac {d_{1}x}{d_{1}x+d_{2}}}\right)^{d_{1}/2}\left(1-{\frac {d_{1}x}{d_{1}x+d_{2}}}\right)^{d_{2}/2}}{x\operatorname {B} (d_{1}/2,d_{2}/2)}}}$

Here, B is the [wikipedia:beta_function Beta function].