consider $n$ iid draws according to some cdf $F$.
What is the probability of the following event: the $k^{\text{th}}$ highest value is smaller than $x$ AND the $k+1$ highest value is larger than $x$.
Thanks for helping out a confused mind.
2026-03-28 05:21:49.1774675309
Probability ( kth order statistics <x , (k+1)th order stat >x)
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Hint: You want the probability that $k$ of the draws are smaller than $x$, and $n-k$ of the draws are larger than $x$, occurring in no particular order.