Question: Find the joint cdf of $Y_1$ and $Y_n$ ($Y_1$ being the first order statistic and $Y_n$ being the maximum).
Find $P(Y_1 >u,Y_n ≤v)$ was given as a hint.
2026-03-26 14:21:04.1774534864
Find the joint CDF of the smallest and largest order statistics $Y_1$ and $Y_n$
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$\Pr(Y_1 >u\ \&\ Y_n ≤v)$ is the probability that all of the $n$ independent identically distributed observations are in the interval $(u,v].$ Since they're independent, this is just the $n$th power of the probability that one of them is in that interval. That probabilty is $F(v) - F(u).$