In question 4.28, it says let $X$ and $Y$ be independent standard normal random variables. Find the distribution of $X/|Y|$. I can understand the answer is Cauchy(0,1) distribution. Then question (c) keeps asking is the answer to part (b) surprising? Can you formulate a general theorem?
For me, it is surprising. Since from Example 4.3.6, I know $X/Y$ is also Cauchy (0,1). Thus $X/Y$ and $X/|Y|$ has the same distribution. I don't know what the authors want to emphasize here. Is there a rule?