The question is as follows:
Let $X_1, . . . , X_{2n}$ be a random sample of $2n$ observations from a standard normal distribution. Let $Y=\frac1n \sum_{i=1}^n X_i$ denote the average of the first $n$ observations $X_1, . . . , X_n$ and let $Z =\frac1n \sum_{i=n+1}^{2n} X_i$ denote the average of the remaining observations $X_{n+1}, . . . , X_{2n}$. Determine the distribution of $\frac{Y}{|Z|}$.