Intuitively obviously, the expectation of the median of sample taken from a $Uniform[a,b]$ distribution is simply $\frac12(b-a)$ but I'm having trouble proving that this is the case. I've shown it for the case $Uniform[0,1]$ and I done that by using the formula for the pmf of the order statistics to find the expectations for them.
2026-02-22 21:28:54.1771795734
Expectation of sample median, general uniform case
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