| Property | Value |
|---|---|
| Hex Value | $BB37 |
| Categories | |
| Localizations |
|
Shadeχ²(
Overview
Draws the density function for the χ² distribution specified by degrees of freedom df, and shades and colors the area between lowerbound and upperbound.
Color#: 10 - 24 or color name pasted from [vars] COLOR.
Availability: Token available everywhere.
Syntax
Shadeχ²(lowerbound,upperbound,df[,color#])
Arguments
| Name | Type | Optional |
|---|---|---|
| χ² | ||
| lowerbound | ||
| upperbound | ||
| df | Yes | |
| color# | colorNum | Yes |
Location
2nd, distr, DRAW, 3:Shade, (
Description
Shadeχ²( is equivalent to χ²cdf( in terms of the probability it calculates: if a random variable follows the χ² distribution, you can use it to calculate the probability that the variable's value falls in a certain interval. However, in addition to calculating the probability, this command also draws the χ² curve, and shades the interval whose area represents the probability you want.
Note that this command does not actually return the value it calculates in Ans or anywhere else: it's merely displayed on the graph. If you're going to use the value in further calculations, you'll have to use χ²cdf( as well.
The Shadeχ²( command takes three arguments. lower and upper identify the interval you're interested in. df specifies the degrees of freedom (selecting from an infinite family of χ² distributions).
Thus, the following code would find the probability of χ² between 0 and 1 on a χ² distribution with 2 degrees of freedom, and shade this interval:
:Shadeχ²(0,1,2
Advanced
Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.
It can be hard to find the best window for Shadeχ²( to work in, since it doesn't automatically zoom for you. For any number of degrees of freedom (except for 1), the graph doesn't go above y=.5 (a good value for Ymax); Ymin should probably be something small and negative. Xmin should be around 0 (possibly slightly less if you like seeing axes), while Xmax probably shouldn't go above 5.
Keep in mind that Shadeχ²( is just a drawing command and not an actual graphed function, so resizing the window, ClrDraw, and other commands that refresh the graphscreen will remove it.
Related Commands
Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.
History
| Calculator | OS Version | Description |
|---|---|---|
| TI-83 | 0.01013 | Added |
Created: February 23, 2023 23:15:01