# tstat

Student's t mean and variance

## Syntax

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

## Description

example

````[m,v] = tstat(nu)` returns the mean and variance of the Student's t distribution with `nu` degrees of freedom.```

## Examples

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

```nu = reshape(1:30,6,5); [m,v] = tstat(nu)```
```m = 6×5 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 = 6×5 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 mean is undefined for `1` degree of freedom, and variance is undefined for `1` and `2` degrees of freedom.

## Input Arguments

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Degrees of freedom for the Student's t distribution, specified as a positive scalar value or an array of positive scalar values.

Example: `[9,19,49,99]`

Data Types: `single` | `double`

## Output Arguments

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Mean of the Student's t distribution with the degrees of freedom specified in `nu`, returned as a scalar value or an array of scalar values. `m` is the same size as `nu`.

Variance of the Student's t distribution with the degrees of freedom specified in `nu`, returned as a scalar value or an array of scalar values. `v` is the same size as `nu`.

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### Mean and Variance of Student’s t Distribution

The parameters of the Student's t distribution depend on the degrees of freedom.

The mean of the Student’s t distribution is μ = 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 $\frac{\nu }{\nu -2}$ for degrees of freedom ν greater than 2. If ν is less than or equal to 2, then the variance is undefined.