# TI-BASIC:Fpdf

**Command Summary**

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

**Command Syntax**

Fpdf(*x*, *numerator df*, *denominator df*)

**Menu Location**

Press:

- 2ND DISTR to access the distribution menu
- 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

<math> \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \operatorname{Fpdf}(x,d_1,d_2) = \frac{\left( \frac{d_1x}{d_1x+d_2} \right)^{d_1/2} \left(1-\frac{d_1x}{d_1x+d_2}\right)^{d_2/2}}{x \operatorname{B}(d_1/2,d_2/2)} </math>

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