The Shadeχ²( Command

Command Summary

Finds the probability of an interval of the χ² distribution, and graphs this distribution with the interval's area shaded.

Command Syntax

Shadeχ²(lower, upper, df)

Menu Location


  1. 2ND DISTR to access the distribution menu
  2. RIGHT to select the DRAW submenu
  3. 3 to select Shadeχ²(, or use arrows

Calculator Compatibility


Token Size

2 bytes

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:



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


Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-Noncommercial-No Derivative Works 2.5 License.