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Let $X_i\in\{0,1\}$ be mutually independent and distributed according to $\mathrm{Bernoulli}(p_i)$ and similarly, $Y_i\sim\mathrm{Bernoulli}(q_i)$, for some parameters $p,q\in[0,1]^n$. Put $X:=\sum_{i=...

We have two arrays $A,B$ of length $n$. All values are i.i.d drawn from same distribution on $[0,1]$. If we sort $A,B$ in non-decreasing order and let $A_{(i)},B_{(i)}$ denote the i-th value in the ...