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# tpdf

Student's t probability density function

Y = tpdf(X,V)

## Description

Y = tpdf(X,V) computes Student's t pdf at each of the values in X using the corresponding degrees of freedom in V. X and V can be vectors, matrices, or multidimensional arrays that have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs.

Student's t pdf is

## Examples

The mode of the t distribution is at x = 0. This example shows that the value of the function at the mode is an increasing function of the degrees of freedom.

```tpdf(0,1:6)
ans =
0.3183  0.3536  0.3676  0.3750  0.3796  0.3827```

The t distribution converges to the standard normal distribution as the degrees of freedom approaches infinity. How good is the approximation for v = 30?

```difference = tpdf(-2.5:2.5,30)-normpdf(-2.5:2.5)
difference =
0.0035  -0.0006  -0.0042  -0.0042  -0.0006  0.0035```