Order Statistics: Expected order statistic of a distribution given an order statistic of a linearly dependent distribution.

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say I have $X \sim \texttt{Binomial}(n, p)$ and $Y \sim \texttt{Binomial}(cn, p)$ where $0 \leq c \leq 1$. Also, I know what $E[W_{X_1}], E[W_{X_2}, ...]$ where $W_{X_i}$ is the $i$th largest sample. I was wondering if there was a straight forward way to get $E[W_{Y_i}]$ where $W_{Y_i}$ is the $i$th largest sample of $Y$?