medium Probability

Large Maxima

A release-checked medium problem for training Uniform, Order Statistics.

Question

Let $X_1,\dots, X_n \sim \unif{0}{1}$, where $n \geq 2$. Let $V = \max\{X_1,\dots, X_n\}$ and $U = \min\{X_1,\dots, X_n\}$. For any $x > 1$, compute $\prob{V/U > x}$. Report the answer when $n = 4$ and $x = 2$.

Practice focus

This Probability problem is tagged Uniform, Order Statistics. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.