Let Xi be a random variable distributed as $N(i, i^2), i = 1, 2, 3$. As-sume that the random variables $X_1, X_2$, and $X_3$ are independent. Using only the three random variables $X_1, X_2$, and $X_3$ give an example of a statistic that has a t distribution with two degrees of freedom.
The definition of a t-distribution that we use in my class is $T= \frac{Z}{\sqrt{U/r}}$ where $U$ is $\chi^2(r)$.
I came up with $\frac{X_1/i}{\sqrt{(X_1+X_2)/2}}$ as an answer, but I just wanted to verify that it's valid or if I'm doing the wrong thing entirely.