The t-distribution

Summary

• If \(Z \sim N(0,1)\) , \(Y \sim χ_k^2\) and \(Z\) and \(Y\) are independent random variables, then we say that

\[T= \frac{Z}{\sqrt{Y/k}}\]

• follows a t-distribution with \(k\) degrees of freedom and we write

\[T \sim t_k\]