Finds the probability for an interval of the χ² distribution.

χ²(*lower*, *upper*, *df*

Press:

- 2ND DISTR to access the distribution menu
- 7 to select χ²cdf(, or use arrows.

Press 8 instead of 7 on a TI-84+/SE with OS 2.30 or higher.

TI-83/84/+/SE

2 bytes

`χ²cdf(` is the χ² cumulative density function. If some random variable follows a χ² distribution, you can use this command to find the probability that this variable will fall in the interval you supply.

The command takes three arguments. *lower* and *upper* define the interval in which you're interested. *df* specifies the degrees of freedom (choosing one of a family of χ² distributions).

# Advanced Uses

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.

The `χ²cdf(` command is crucial to performing a χ² goodness of fit test, which the early TI-83 series calculators do not have a command for (the `χ²-Test(` command performs the χ² test of independence, which is not the same thing, although the manual always just refers to it as the "χ² Test"). This test is used to test if an observed frequency distribution differs from the expected, and can be used, for example, to tell if a coin or die is fair.

The Goodness-of-Fit Test routine on the routines page will perform a χ² goodness of fit test for you. Or, if you have a TI-84+/SE with OS version 2.30 or higher, you can use the `χ²GOF-Test(` command.

# Formulas

As with other continuous distributions, we can define `χ²cdf(` in forms of the probability density function:

# Related Commands

# See Also

.