easy Probability

Maximin Uniform

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

Question

Let $X_{1},...,X_{n}$ be independent and identically distributed $\unif{0}{1}$ random variables. If we denote $Z = \text{max}(X_{1},...,X_{n})$ and $W = \text{min}(X_{1},...,X_{n})$, what is the value of $f_{Z,W}(0.7,0.5)$ when $n = 5$, where $f_{Z,W}(z,w)$ is the joint pdf of $Z$ and $W$.

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.