easy Probability

Maxima Range

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

Question

Suppose that $X_1,\dots, X_n \sim \unif{0}{a}$ for some $a > 0$. Define $M_n = \max(X_1,\dots, X_n)$. For $(b,c] \subseteq (0,a)$, compute $\prob{b < M_n \leq c}$ when $n = 4, a = 5,$ and $(b,c] = (2,4]$.

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.