# Documentation

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# tstat

Student's t mean and variance

## Syntax

```[m,v] = tstat(nu) ```

## Description

`[m,v] = tstat(nu)` returns the mean of and variance for Student's t distribution using the degrees of freedom in `nu`. `nu` can a vectors, matrix, or multidimensional array. The returned values for `m` and `v` are the same size as `nu`.

## Examples

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Compute the mean and variance for Student's t distributions with degrees of freedom nu equal to 1 through 30.

```nu = reshape(1:30,6,5); [m,v] = tstat(nu) ```
```m = NaN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 v = NaN 1.4000 1.1818 1.1176 1.0870 NaN 1.3333 1.1667 1.1111 1.0833 3.0000 1.2857 1.1538 1.1053 1.0800 2.0000 1.2500 1.1429 1.1000 1.0769 1.6667 1.2222 1.1333 1.0952 1.0741 1.5000 1.2000 1.1250 1.0909 1.0714 ```

Note that the variance does not exist for one and two degrees of freedom.

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### Student’s t Mean and Variance

The mean of the Student’s t distribution is

`$\text{mean}=0$`

for degrees of freedom ν greater than 1. If ν equals 1, then the mean is undefined.

The variance of the Student’s t distribution is

`$\mathrm{var}=\frac{\nu }{\nu -2}$`

for degrees of freedom ν greater than 2. If ν is less than or equal to 2, then the variance is undefined.