Let \(U, V \sim_{\text {iid }} \mathscr{U}(0,1)\). The reason why in Example 3.

7 the sample mean and sample median behave very differently is that \(\mathbb{E}[U / V]=\infty\), while the median of \(U / V\) is finite. Show this, and compute the median. [Hint: start by determining the cdf of \(Z=U / V\) by writing it as an expectation of an indicator function.]