# Student t Distribution

Assume that a random variable Z has the standard normal distribution, and another random variable V has the Chi-Squared distribution with m degrees of freedom. Assume further that Z and V are independent, then the following quantity follows a Student t distribution with m degrees of freedom.

Here is a graph of the Student t distribution with 5 degrees of freedom.

#### Problem

Find the 2.5^{th} and 97.5^{th} percentiles of the Student t distribution with 5 degrees of
freedom.

#### Solution

We apply the quantile function qt of the Student t distribution against the decimal values 0.025 and 0.975.

#### Answer

The 2.5^{th} and 97.5^{th} percentiles of the Student t distribution with 5 degrees of
freedom are -2.5706 and 2.5706 respectively.