= Expected number of coordinatewise maxima
{title2=$\mathbb E K_n=H_n$}
For $n$ independent uniform points in a rectangle, condition on one point with normalized coordinates $(x,y)$. It is a <maximal external point> if all others avoid the upper-right rectangle of area $(1-x)(1-y)$, giving conditional probability $[1-(1-x)(1-y)]^{n-1}$. Integrating gives $H_n/n$, where $H_n$ is a <harmonic number>. <Linearity of expectation> over the $n$ <indicator random variables> gives $\mathbb E K_n=H_n$. The same answer holds for independent continuous coordinate distributions, by transforming each coordinate with its distribution function.
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