Suppose we have ordered numbers $a_1 < a_2 < \dots < a_n$. Now we sample $k$ of them with equal probability and with replacement and compute the median of these and call it $m$. (Let us assume that $k$ is odd for the sake of simplicity.) What is the probability the $m = a_i$ for each $i$?

I want to know this to construct the probability mass function for the median of $k$ random draws from a sample of $n$ numbers.

(Already asked here but does not seem to be simple.)


closed as off-topic by Matt F., user44191, LSpice, Pace Nielsen, YCor May 10 at 8:20

This question appears to be off-topic. The users who voted to close gave these specific reasons:

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  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – Matt F., user44191
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  • 2
    $\begingroup$ I think this belongs on MathStackExchange, and I answered it there. $\endgroup$ – Matt F. May 7 at 11:53
  • $\begingroup$ Thanks for answering on MathStackExchange (find link in question)! $\endgroup$ – janlo May 8 at 8:55